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group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) congruence function field; automorphism group; Galois group; ramification Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Representations of groups as automorphism groups of algebraic systems Groups of automorphisms of global function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hasse-Witt matrix of an algebraic curve Manin, Y.I.; The Hasse-Witt Matrix of an Algebraic Curve; Izv. Akad. Nauk SSSR Ser. Mat.: 1961; Volume 25 ,153-172. Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Arithmetic algebraic geometry (Diophantine geometry) On the Hasse-Witt matrix of an algebraic curve
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Tate module; arithmetic fundamental group; Galois representation; Fontaine-Mazur conjecture; cyclic covering; rational point; Galois group of function field; large quotient; moduli space of abelian varieties G. Frey and E. Kani, Projective p-adic representations of the k-rational geometric fundamental group, Archiv der Mathematik 77 (2001), 32--46. Coverings of curves, fundamental group, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic functions and function fields in algebraic geometry, Rational points Projective \(p\)-adic representations of the \(K\)-rational geometric fundamental group
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) general linear groups; arithmetic subgroups; Bruhat-Tits trees; quotient graphs; maximal orders; representation fields L. ÂRENAS-CARMONA, Computing quaternion quotient graphs via~representations of orders, J. Algebra. 402, pp. 258-279, (2014). Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Groups acting on trees, Linear algebraic groups over global fields and their integers Computing quaternion quotient graphs via representations of orders
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois line; Galois point; Artin-Schreier-Mumford curve; automorphism group Plane and space curves, Automorphisms of curves, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields Galois lines for the Artin-Schreier-Mumford curve
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) purely cubic function field; fractional ideal; basis reduction Scheidler, R.''Reduction in Purely Cubic Function Fields of Unit Rank One.''515--532. 2000Berlin: Springer-Verlag. [Scheidler 00], In Proc. Fourth Algorithmic Number Theory Symp. ANTS-IV, Lect. Notes Comp. Sci. 1838 Arithmetic theory of algebraic function fields, Number-theoretic algorithms; complexity, Cubic and quartic extensions, Algebraic functions and function fields in algebraic geometry Reduction in purely cubic function fields of unit rank one
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Pell's equation; local global principle; unlikely intersections Quadratic and bilinear Diophantine equations, Abelian varieties of dimension \(> 1\), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic functions and function fields in algebraic geometry Pell's equation in polynomials and additive extensions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) theory of algebraic curves; coding theory; Riemann-Roch theorem; function fields; differentials; Hasse-Weil theorem; geometric Goppa codes; trace codes H. Stichtenoth, Algebraic Function Fields and Codes, Second edn, (Springer-Verlag, Berlin Heidelberg, 2009). Zbl0816.14011 MR2464941 Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory, Research exposition (monographs, survey articles) pertaining to information and communication theory, Geometric methods (including applications of algebraic geometry) applied to coding theory, Cyclic codes Algebraic function fields and codes
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) tame ramification; Coates algorithm; elements of bounded norm; global function field; reduced integral bases; Puiseux series; Riemann-Roch space; successive minima; unit group; torsion units; root tests Schörnig, M., 1996. Untersuchungen konstruktiver Probleme in globalen Funktionenkörpern. Thesis. TU Berlin Arithmetic theory of algebraic function fields, Units and factorization, Algebraic number theory computations, Algebraic functions and function fields in algebraic geometry Studies of constructive problems in global function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) minimal number of multisets; \(m\)-valued algebraic function A. A. Goldberg and V. A. Pyana, ?The uniqueness theorems for algebraic functions,?Entire and Subharmonic Functions. Advances in Soviet Mathematics,11, 119-204 (1992). Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Uniqueness theorems for algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Kummer extension; rational function field; splitting of prime divisors; genus; smooth projective curve Xing, C. P.: Multiple Kummer Extensions and the Number of Prime Divisors of Degree One in Function Fields. J. of Pure and Appl. Algebra84, 85--93 (1993) Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic coding theory; cryptography (number-theoretic aspects), Algebraic functions and function fields in algebraic geometry Multiple Kummer extension and the number of prime divisors of degree one in function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Proceedings, conferences, collections, etc. pertaining to number theory, Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to information and communication theory, Curves over finite and local fields, Arithmetic theory of algebraic function fields, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Algebraic coding theory; cryptography (number-theoretic aspects), Algebraic functions and function fields in algebraic geometry, Families, moduli of curves (algebraic), Automorphisms of curves, Cryptography, Shift register sequences and sequences over finite alphabets in information and communication theory, Semifields, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) Algebraic curves and finite fields. Cryptography and other applications. results of the workshops ``Applications of algebraic curves'' and ``Applications of finite fields'' of the RICAM Special Semester 2013
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) division algebras; Brauer groups; rational function fields; ramification maps; central simple algebras A. S. Sivatski, L. H. Rowen and J.-P. Tignol, Division algebras over rational function fields in one variable, in Algebra and Number Theory, Proceedings of the Silver Jubilee Conference 2003, Hindustan Book Agency, New Delhi, 2005, pp. 158--180. Finite-dimensional division rings, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Division algebras over rational function fields in one variable.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic functions; algebraic number fields Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Riemann surfaces The theory of algebraic functions of one variable.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism groups of algebraic function fields; realization of group as Galois group; Galois theory Henning Stichtenoth, Zur Realisierbarkeit endlicher Gruppen als Automorphismengruppen algebraischer Funktionenkörper, Math. Z. 187 (1984), no. 2, 221 -- 225 (German). Separable extensions, Galois theory, Inverse Galois theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Zur Realisierbarkeit endlicher Gruppen als Automorphismengruppen algebraischer Funktionenkörper
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) absolute Galois group of rational function field; real closed field; Tarski principle; transfer principle L P.D. v.d. Dries and P. Ribenboim , An application of Tarski's principle to absolute Galois groups of function fields , Queen's Mathematical Preprint No. 1984-8. Separable extensions, Galois theory, Ultraproducts and field theory, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Real algebraic and real-analytic geometry An application of Tarski's principle to absolute Galois groups of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Function field; Jacobian; \(\ell\)-rank; L-polynomial Berger, Lisa; Hoelscher, Jing Long; Lee, Yoonjin; Paulhus, Jennifer; Scheidler, Renate: The \(\ell \)-rank structure of a global function field, Fields inst. Commun. 60, 145-166 (2011) Arithmetic theory of algebraic function fields, Class groups and Picard groups of orders, Algebraic number theory computations, Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry The \(\ell\)-rank structure of a global function field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; homogeneous unit equation; derivations on function fields D. BROWNAWELL - D. MASSER, Vanishing sums in function fields, Math. Proc. Camb. Phil. Soc., 100 (1986), pp. 427-434. Zbl0612.10010 MR857720 Higher degree equations; Fermat's equation, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Vanishing sums in function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic complexity; fast polynomial multiplication; multiplicative complexity; linear coding; algebraic curves over finite fields Chudnovsky, D. V., Chudnovsky, G. V.: Algebraic complexities and algebraic curves over finite fields. Proc. Natl. Acad. Sci. USA84, 1739--1743 (1987) Analysis of algorithms and problem complexity, Software, source code, etc. for problems pertaining to field theory, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields Algebraic complexities and algebraic curves over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Lang S: \textit{Elliptic Functions}. 2nd edition. Springer, New York; 1987. Curves in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic theory of algebraic function fields, Modular and automorphic functions, Algebraic functions and function fields in algebraic geometry, Complex multiplication and moduli of abelian varieties, Complex multiplication and abelian varieties, Research exposition (monographs, survey articles) pertaining to field theory Elliptic functions. Second edition
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) quadratic algebraic function fields; divisor class number two Le Brigand, D.: Classification of algebraic function fields with divisor class number two. Finite fields appl. 2, 153-172 (1996) Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry Classification of algebraic function fields with divisor class number two
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism groups of function fields; function fields over finite fields Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Automorphisms of curves, Applications to coding theory and cryptography of arithmetic geometry The asymptotic behavior of automorphism groups of function fields over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function field; quadratic field; ideal class group Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry, Quadratic extensions On imaginary quadratic function fields with ideal class group of exponent \(\leq 2\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; Weil differentials; Weierstrass points; Riemann hypothesis; zeta functions; coding theory Goldschmidt, D. M.: Algebraic functions and projective curves, Grad texts in math. 215 (2003) Algebraic functions and function fields in algebraic geometry, Zeta functions and \(L\)-functions of number fields, Arithmetic theory of algebraic function fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Applications to coding theory and cryptography of arithmetic geometry Algebraic functions and projective curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois tower; modular tower; Galois closure; function field Bassa, A.; Beelen, P.: On the construction of Galois towers, Contemp. math. 487, 9-20 (2009) Algebraic functions and function fields in algebraic geometry, Galois theory, Arithmetic theory of algebraic function fields, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) On the construction of Galois towers
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) hyperelliptic function fields; imaginary quadratic function field; real quadratic function field; divisor class group; reduced ideals; group law [14]S. Paulus and H.-G. Rück, Real and imaginary quadratic representations of hyperelliptic function fields, Math. Comput. 68 (1999), 1233--1241. Arithmetic theory of algebraic function fields, Class groups and Picard groups of orders, Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry Real and imaginary quadratic representations of hyperelliptic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Singh B. On the group of automorphisms of a function field of genus at least two. J Pure Appl Algebra, 4: 205--229 (1975) Arithmetic theory of algebraic function fields, Ramification and extension theory, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry On the group of automorphisms of a function field of genus at least two
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function field; automorphism group Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Representations of groups as automorphism groups of algebraic systems On Galois groups of global fields of positive characteristic
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic number theory; valuation theory; local class field theory; algebraic number fields; algebraic function fields of one variable; Riemann-Roch theorem E. Artin, Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967. Research exposition (monographs, survey articles) pertaining to number theory, Class field theory, Class field theory; \(p\)-adic formal groups, Ramification and extension theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Collected or selected works; reprintings or translations of classics Algebraic numbers and algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; class number one; Weil polynomials Arithmetic theory of algebraic function fields, Curves over finite and local fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry The relative class number one problem for function fields. I
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) valued function fields; good reduction; regular functions; reciprocity lemma; unit; local symbols; local-global principle; solvability of diophantine equations P. Roquette, \textsl Reciprocity in valued function fields, Journal für die reine und angewandte Mathematik 375/376 (1987), 238--258. Arithmetic theory of algebraic function fields, Valued fields, Algebraic functions and function fields in algebraic geometry, Diophantine equations Reciprocity in valued function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) transcendental field extensions; Galois group; elliptic function fields Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Transcendental field extensions, Galois theory Un exemple de groupe de Galois d'une extension transcendante
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves; finite ground field; minimal algebraic complexities; multiplication; algebras over finite fields; coding theory; algebraic geometrical methods; Goppa codes D. V. Chudnovsky and G. V. Chudnovsky, ''Algebraic complexities and algebraic curves over finite fields,'' J. Complexity, 4, 285--316 (1988). Analysis of algorithms and problem complexity, Arithmetic codes, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Arithmetic ground fields for curves, Algebraic functions and function fields in algebraic geometry, Riemann-Roch theorems Algebraic complexities and algebraic curves over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic functions in two variables; Riemann-Roch theorem; function fields Heinrich W. E. Jung, Einführung in die Theorie der algebraischen Funktionen zweier Veränderlicher, Akademie Verlag, Berlin, 1951 (German). Arithmetic theory of algebraic function fields, Research exposition (monographs, survey articles) pertaining to number theory, Algebraic functions and function fields in algebraic geometry Einführung in die Theorie der algebraischen Funktionen zweier Veränderlicher
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) K. Feng and W. Gao, Bernoulli-Goss polynomials and class numbers of cyclotomic function fields, preprint. Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Cyclotomic extensions, Special polynomials in general fields, Algebraic functions and function fields in algebraic geometry Bernoulli-Goss polynomial and class number of cyclotomic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) tower of function fields; genus; rational places; curves with many points A. Garcia, H. Stichtenoth, On the Galois closure of towers, preprint, 2005 Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry Asymptotics for the genus and the number of rational places in towers of function fields over a finite field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois groups of function fields; unramified cohomology; universal spaces; anabelian geometry Galois cohomology, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Cohomology of groups Universal spaces for unramified Galois cohomology
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cubic function fields; ramification; families; explicit aspects Cubic and quartic extensions, Arithmetic theory of algebraic function fields, Quadratic extensions, Algebraic functions and function fields in algebraic geometry, Families, moduli of curves (algebraic) Cubic function fields with prescribed ramification
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Riemann surfaces; Abelian integrals; algebraic number theory; function fields; valuations; function fields of curves; Abel-Jacobi theorem Cohn, P. M.: Algebraic numbers and algebraic functions, Chapman \& Hall math. Ser. (1991) Algebraic number theory: global fields, Arithmetic theory of algebraic function fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Algebraic functions and function fields in algebraic geometry Algebraic numbers and algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) absolutely irreducible polynomials; algebraic functions; Hilbert irreducibility theorem Hilbertian fields; Hilbert's irreducibility theorem, Polynomials in general fields (irreducibility, etc.), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Independence of values of algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) division algebra over function field; sheaf of differentials; maximal order; Riemann-Roch theorem; genus M. van den Bergh and J. Van Geel, Algebraic elements in division algebras over function fields of curves, Israel J. Math., 52 (1985), no. 1-2, 33--45. Zbl 0596.12012 MR 0815599 Quaternion and other division algebras: arithmetic, zeta functions, Transcendental field extensions, Skew fields, division rings, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Arithmetic theory of algebraic function fields, Division rings and semisimple Artin rings, Algebraic functions and function fields in algebraic geometry Algebraic elements in division algebras over function fields of curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) noncommutative regular projective curve; noncommutative function field; Auslander-Reiten translation; Picard-shift; ghost group; maximal order over a scheme; ramification; Witt curve; noncommutative elliptic curve; Klein bottle; Fourier-Mukai partner; weighted curve; orbifold Euler characteristic; noncommutative orbifold; tubular curve; finite dimensional algebra; Beilinson theorem Kussin, Dirk, Weighted noncommutative regular projective curves, J. Noncommut. Geom., 10, 4, 1465-1540, (2016) Noncommutative algebraic geometry, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers, Abelian categories, Grothendieck categories, Elliptic curves, Orders in separable algebras, Klein surfaces Weighted noncommutative regular projective curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Giulietti-Korchmáros maximal curve; Weierstrass semigroup; Weierstrass points Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences Weierstrass semigroups on the Giulietti-Korchmáros curve
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Wagner, M.: Über korrespondenzen zwischen algebraischen funktionenkörpern, (2009) Computational aspects of algebraic curves, Arithmetic ground fields for curves, Coverings of curves, fundamental group, Special algebraic curves and curves of low genus, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic theory of algebraic function fields On correspondences between algebraic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) valued fields; rigid analytic spaces; algebraic curves; constant reduction Valued fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Recent results in the theory of constant reductions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) global function fields; curves with many rational points; low-discrepancy sequences; Gilbert-Varshamov bound Niederreiter, H., Xing, Ch.: Global function fields with many rational places and their applications. In: Mullin, R.C., Mullen, G.L. (eds.) Finite Fields: Theory, Applications, and Algorithms, Waterloo, ON, 1997. Contemp. Math., vol. 225, pp. 87--111. Amer. Math. Soc., Providence (1999) Curves over finite and local fields, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Global function fields with many rational places and their applications
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) towers of algebraic function fields; genus; number of places Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Quadratic recursive towers of function fields over \(\mathbb{F}_2\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) higher derivations; algebraic function field; Taylor expansion Morphisms of commutative rings, Modules of differentials, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Higher derivations of algebraic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field of one variable over a finite field; group of divisor classes; upper bound; zeta-function Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry Divisorklassen der Ordnung \(\ell\) bei Kongruenzfunktionenkörpern
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) composite rational function; lacunary polynomial Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On composite rational functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curve; \(L\)-function; quadratic twist; rational function; sum of \(L\)-functions B. Fisher and S. Friedberg, Double Dirichlet series over function fields, Compositio Mathematica 140 (2004), 613--630. Zeta and \(L\)-functions in characteristic \(p\), Curves over finite and local fields, Gauss and Kloosterman sums; generalizations, Estimates on exponential sums, Other analytic theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Double Dirichlet series over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) quadratic point; bielliptic curve; hyperelliptic curve; modular curves Harris, J.; Silverman, J. H., \textit{bielliptic curves and symmetric products}, Proc. Amer. Math. Soc., 112, 347-356, (1991) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic functions and function fields in algebraic geometry, Arithmetic aspects of modular and Shimura varieties Bielliptic curves and symmetric products
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function field; Kummer extension; genus field; Hilbert extension Peng G.: The genus fields of Kummer function fields. J. Number Theory 98, 221--227 (2003) Other abelian and metabelian extensions, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry The genus fields of Kummer function fields.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) generators; equations; modular function fields; principal congruence subgroups; minimal polynomials N. Ishida, Generators and equations for modular function fields of principal congruence subgroups. Acta Arith. 85 (1998), no. 3, 197-207. Zbl0915.11025 MR1627819 Modular and automorphic functions, Algebraic functions and function fields in algebraic geometry, Holomorphic modular forms of integral weight, Curves of arbitrary genus or genus \(\ne 1\) over global fields Generators and equations for modular function fields of principal congruence subgroups
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mordell-Weil group; procyclic extension of rational function field; elliptic curves over function fields Fastenberg, L., Mordell-Weil groups in procyclic extensions of a function field, Ph.D. Thesis, Yale University, 1996. Rational points, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Elliptic curves over global fields, Elliptic curves Mordell-Weil groups in procyclic extensions of a function field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Gál's sums; Dirichlet polynomials; Riemann zeta function; Dirichlet \(L\)-functions; resonance method; function fields Zeta functions and \(L\)-functions of function fields, \(\zeta (s)\) and \(L(s, \chi)\), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Large values of Dirichlet \(L\)-functions over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Artin-Schreier extension; compositum; decomposition law; different; ramification group Wu, Q.; Scheidler, R., The ramification groups and different of a compositum of Artin-Schreier extensions, Int. J. Number Theory, 6, 1541-1564, (2010) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Other abelian and metabelian extensions, Special algebraic curves and curves of low genus The ramification groups and different of a compositum of Artin-Schreier extensions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function field; group of automorphisms; finiteness; Weierstrass points Schmid, Über die Automorphismen eines algebraischen Funktionenkörpers von Primzahlcharakteriatik., J. reine angew. Math. 179 pp 5-- (1938) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Automorphisms of curves, Riemann surfaces; Weierstrass points; gap sequences Über die Automorphismen eines algebraischen Funktionenkörpers von Primzahlcharakteristik
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Drinfeld module; Drinfeld modular curve; Ihara's quantity; BBGS tower Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry A modular interpretation of BBGS towers
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) composite rational functions; lacunary polynomials; arithmetic progressions Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Composite rational functions and arithmetic progressions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) elliptic curve; elliptic surface; function field; genus; gonality; \(p\)-rank; torsion; K3 surface Andreas Schweizer, On the \?^{\?}-torsion of elliptic curves and elliptic surfaces in characteristic \?, Trans. Amer. Math. Soc. 357 (2005), no. 3, 1047 -- 1059. Elliptic curves over global fields, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Elliptic curves, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Curves over finite and local fields, Global ground fields in algebraic geometry, \(K3\) surfaces and Enriques surfaces On the \(p^e\)-torsion of elliptic curves and elliptic surfaces in characteristic \(p\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Brauer groups; \(n\)-Brauer dimension; \(\mathbb Z/n\)-cyclic classes; \(\mathbb Z/n\)-lengths; connected regular projective relative curves; divisors; hot points; finitely-generated extensions of transcendence degree \(1\); Brauer equivalence classes of cyclic algebras; central division algebras E. Brussel and E. Tengan, Division algebras of prime period \( \ell \neq p\) over function fields of \( p\)-adic curves, Israel J. Math. (to appear). Finite-dimensional division rings, Curves over finite and local fields, Arithmetic theory of algebraic function fields, Skew fields, division rings, Local ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Brauer groups (algebraic aspects) Tame division algebras of prime period over function fields of \(p\)-adic curves.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebra, number theory Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Das arithmetische Geschlecht
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) number fields, function fields S. Arima: Certain generators of non-hyperelliptic fields of algebraic functions of genus ^3, Proc. Japan Acad., 36, 6-9 (1960). Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Certain generators of non-hyperelliptic fields of algebraic functions of genus \(\geq 3\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Belyi's theorems; function field; finite field; tame and wild ramification; pseudo-tame Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry Belyi's theorems in positive characteristic
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) ray class fields; global function fields; curves with many rational points; S-class numbers Auer, Roland, Ray class fields of global function fields with many rational places, Acta Arith., 95, 97-122, (2000) Arithmetic theory of algebraic function fields, Class field theory, Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields, Finite ground fields in algebraic geometry, Algebraic number theory computations, Class numbers, class groups, discriminants Ray class fields of global function fields with many rational places
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) abstract elliptic function fields; divisor class group of finite order; automorphisms; meromorphisms; addition theorems; structure of ring of meromorphisms; Riemann hypothesis Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Zur Theorie der abstrakten elliptischen Funktionenkörper. I: Die Struktur der Gruppe der Divisorenklassen endlicher Ordnung. II: Automorphismen und Meromorphismen. Das Additionsproblem. III: Die Struktur des Meromorphismenrings. Die Riemannsche Ver\-mutung.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational points; function fields; characteristic p; curves; abelian varieties Varieties over global fields, Arithmetic theory of algebraic function fields, Arithmetic varieties and schemes; Arakelov theory; heights, Global ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry Bounds for the number of rational points on curves over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; moduli Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Families, moduli of curves (algebraic) Moduli of a field of algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field; power series Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields Gaps in Taylor series of algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; Bombieri-lang conjecture; varieties of general type Rational points, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Rational points of varieties with ample cotangent bundle over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function fields; finite field of constants; Severi's algebraic theory of correspondences; Hurwitz's transcendental theory; group of divisor classes; Riemann hypothesis for function fields; action of Galois group André Weil, Sur les fonctions algébriques à corps de constantes fini, C. R. Acad. Sci. Paris 210 (1940), 592 -- 594 (French). Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves, Finite ground fields in algebraic geometry Sur les fonctions algébriques à corps de constantes fini
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function fields; Riemann-Roch theorem Witt, E.: Riemann--Rochscher Satz und {\(\zeta\)}-Funktion im Hyperkomplexen. Math. Ann. 110, 12--28 (1934) Riemann-Roch theorems, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Riemann-Rochscher Satz und \(Z\)-Funktion im Hyperkomplexen
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(p\)-extensions of algebraic function fields; Artin-Schreier theory; characteristic \(p\); genus; number of rational points; coding theory; gap number Arnaldo Garcia and Henning Stichtenoth, Elementary abelian \(p\)-extensions of algebraic function fields, Manuscr. Math. 72 (1991), 67--79. Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Geometric methods (including applications of algebraic geometry) applied to coding theory, Riemann surfaces; Weierstrass points; gap sequences, Computational aspects of algebraic curves Elementary abelian \(p\)-extensions of algebraic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Automorphism of function fields; singular points; rational function fields. Automorphisms of curves, Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry A relation between Galois automorphism and curve singularity
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) multiplicator ring; elliptic function fields Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Die Typen der Multiplikatorenringe elliptischer Funktionenkörper.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function field; effective divisors Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry On the number of effective divisors in algebraic function fields defined over a finite field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves; algebraic function fields; maximal curves; maximal function fields; automorphisms of function fields Güneri, C.; Özdemir, M.; Stichtenoth, H., The automorphism group of the generalized giulietti-korchmáros function field, \textit{Adv. Geom.}, 13, 369-380, (2013) Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry The automorphism group of the generalized Giulietti-Korchmáros function field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Riemann hypothesis; global function fields; zeta function in characteristic \(p\), Emil Artin; Helmut Hasse; André Weil; Friedrich Karl Schmidt; Max Deuring Research exposition (monographs, survey articles) pertaining to number theory, History of number theory, History of algebraic geometry, Arithmetic theory of algebraic function fields, Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, History of mathematics in the 20th century, Sociology (and profession) of mathematics, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Algebraic functions and function fields in algebraic geometry The Riemann hypothesis in characteristic \(p\) in historical perspective
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) S. O. Gorchinskii, ``Poincare\' biextension and ide\?les on an algebraic curve'', Sb. Math., 197:1 (2006), 23 -- 36 Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Extensions, wreath products, and other compositions of groups, Jacobians, Prym varieties, Arithmetic ground fields for curves Poincaré biextension and idèles on an algebraic curve
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mordell-Weil group; multidimensional function fields; Néron-Tate height; Mordell-Weil rank; Jacobian; independence of some rational points T. Shioda, Constructing curves with high rank via symmetry, Amer. J. Math., to appear. Algebraic functions and function fields in algebraic geometry, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields Constructing curves with high rank via symmetry
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) m-division points; m-division fields; elliptic curve; primitive torsion point; characteristic p Special algebraic curves and curves of low genus, Elliptic curves, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Galois theory On the structure of elliptic fields. I
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) arithmetic symbols; reciprocity laws; discrete valuation field; linear group; algebraic curve Pablos Romo, F, Central extensions, symbols and reciprocity laws on \(\operatorname{GL}(n,\tilde{\mathcal{F}})\), Pac. J. Math., 234, 137-159, (2008) Symbols and arithmetic (\(K\)-theoretic aspects), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Central extensions, symbols and reciprocity laws on \(\mathrm{GL}(n,\mathcal F)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; unit equation; diagonal equation; Weierstrass points Voloch, José Felipe, Diagonal equations over function fields, Bol. Soc. Brasil. Mat., 0100-3569, 16, 2, 29-39, (1985) Higher degree equations; Fermat's equation, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Diagonal equations over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) global function fields; rational places; curves over finite fields; lower bound for \(A(2), A(3)\); class field towers; Drinfel'd-Vlădut bound Angles B., Maire C.: A note on tamely ramified towers of global function fields. Finite Field Appl. \textbf{8}, 207-215 (2002). Curves over finite and local fields, Arithmetic theory of algebraic function fields, Class field theory, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Rational points, Arithmetic ground fields for curves A note on tamely ramified towers of global function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Drinfeld modules; Erdős-Pomerance's conjecture Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On an Erdős-pomerance conjecture for rank one Drinfeld modules
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Proceedings, conferences, collections, etc. pertaining to number theory, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Abelian varieties of dimension \(> 1\), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Transcendence theory of Drinfel'd and \(t\)-modules, Iwasawa theory, \(p\)-adic cohomology, crystalline cohomology, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Proceedings of conferences of miscellaneous specific interest Arithmetic geometry over global function fields. Selected notes based on the presentations at five advanced courses on arithmetic geometry at the Centre de Recerca Matemàtica, CRM, Barcelona, Spain, February 22 -- March 5 and April 6--16, 2010
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mumford representation; hyperelliptic curve Platonov, V. P.; Zhgun, V. S.; Fedorov, G. V., Continued rational fractions in hyperelliptic fields and the Mumford representation, Dokl. Ross. Akad. Nauk, 471, 6, 640-644, (2016) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Special divisors on curves (gonality, Brill-Noether theory), Continued fractions and generalizations Continued rational fractions in hyperelliptic fields and the Mumford representation
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) polynomial with integral coefficients; Dickson numbers; permutation property; monodromy group; algebraic function Kurbatov V. A. Über die Monodromiegruppe einer algebraischen Funktion. Mat. Sbornik, n. Ser.25 (65), (1949), 51-94 (russisch). Polynomials in number theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On the monodromy group of an algebraic function
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) transcendence in finite characteristic; six exponentials theorem Arithmetic theory of algebraic function fields, Transcendence (general theory), Formal groups, \(p\)-divisible groups, Algebraic functions and function fields in algebraic geometry A six exponentials theorem in finite characteristic
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic geometric codes; self-dual codes; algebraic function field; geometric Goppa code Driencourt, Y.; Stichtenoth, H.: A criterion for self-duality of geometric codes. Comm. algebra 17, 885-898 (1989) Linear codes (general theory), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry A criterion for self-duality of geometric codes
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) imaginary quadratic function fields; class numbers; JFM 50.0107.01 Brigand, D.: Quadratic algebraic function fields with ideal class number two. Arithmetic geometry and coding theory, luminy, 1993, 105-126 (1996) Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry Quadratic algebraic function fields with ideal class number two
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) quinary field; curves with many rational points; global function fields; finite field; many rational places; Hilbert class field; hyperelliptic function field Arithmetic theory of algebraic function fields, Curves over finite and local fields, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Rational points Global function fields with many rational places over the quinary field. II
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) abelian varieties; abelian surface; abelian function field; Enriques surface , Galois subfields of abelian functon field of two variables, Proc. Japan Acad., 70 (1994), 3-5. Analytic theory of abelian varieties; abelian integrals and differentials, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for abelian varieties, Arithmetic theory of algebraic function fields, Other abelian and metabelian extensions Galois subfields of abelian function field of two variables
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic functions; minimal degree of a field; lower bound irreducible polynomials Pierre D`ebes, On a problem of Dvornicich and Zannier, Acta Arith. 73 (1995), no. 4, 379--387. MR1366044 Hilbertian fields; Hilbert's irreducibility theorem, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Polynomials in general fields (irreducibility, etc.) On a problem of Dvornicich and Zannier
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Drinfeld modules; elliptic sheaves; elliptic modules; level structure; central simple algebra; moduli spaces; reciprocity law; local Langlands conjecture; Selberg trace formula; Grothendieck-Lefschetz fixed point formula; Tate conjectures Laumon, G.; Rapoport, M.; Stuhler, U., \(\mathcal{D}\)-elliptic sheaves and the Langlands correspondence, Invent. Math., 113, 217-338, (1993) Drinfel'd modules; higher-dimensional motives, etc., Algebraic functions and function fields in algebraic geometry, Langlands-Weil conjectures, nonabelian class field theory, Finite ground fields in algebraic geometry, Spectral theory; trace formulas (e.g., that of Selberg), Arithmetic theory of algebraic function fields, Formal groups, \(p\)-divisible groups \({\mathcal D}\)-elliptic sheaves and the Langlands correspondence
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Tamagawa numbers; Weil's Conjecture; moduli stack Research exposition (monographs, survey articles) pertaining to algebraic geometry, \(p\)-adic cohomology, crystalline cohomology, Arithmetic theory of algebraic function fields, Vector bundles on curves and their moduli, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Algebraic functions and function fields in algebraic geometry, Algebraic moduli problems, moduli of vector bundles Weil's conjecture for function fields: volume I
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function field; Cartier operator; Weierstrass gap sequences; Hasse-Witt matrix Stöhr, K. O.; Viana, P.: A study of Hasse--Witt matrices by local methods. Math. Z. 200, 397-407 (1989) Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences, Arithmetic theory of algebraic function fields, Divisors, linear systems, invertible sheaves A study of Hasse-Witt matrices by local methods
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Iwasawa function; Igusa curves; Kubota-Leopoldt p-adic L-function; Iwasawa ring; Hecke algebra; Teichmüller character; function field; diamond operator; vanishing of \(\mu\)-invariant; Igusa-regularity; proalgebraic of Weil type; Frobenius endomorphism Mazur, B.; Wiles, A., \textit{analogies between function fields and number fields}, Amer. J. Math., 105, 507-521, (1983) Zeta functions and \(L\)-functions, Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Zeta functions and \(L\)-functions of number fields, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Jacobians, Prym varieties Analogies between function fields and number fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) ramification of algebraic functions; characteristic two Shreeram Abhyankar, Ramification theoretic methods in algebraic geometry, Annals of Mathematics Studies, no. 43, Princeton University Press, Princeton, N.J., 1959. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On the ramification of algebraic functions. II: Unaffected equations for characteristic two
| 0 |
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