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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 \(x^n+y^m+1=0\) quasirandom point; digital net; Hammersley net Niederreiter, H.: Finite fields and quasirandom points. In: Charpin, P., Pott, A., Winterhof, A. (eds.) Finite Fields and Their Applications: Character Sums and Polynomials, pp. 169--196. de Gruyter, Berlin (2013) Pseudo-random numbers; Monte Carlo methods, Orthogonal arrays, Latin squares, Room squares, Irregularities of distribution, discrepancy, Arithmetic theory of algebraic function fields, Polynomials over finite fields, Algebraic functions and function fields in algebraic geometry, Monte Carlo methods Finite fields and quasirandom points
| 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 \(x^n+y^m+1=0\) variety of subfields; stable points; automorphism action; moduli space; rational function field; affine algebraic variety; Bezout form Arithmetic theory of algebraic function fields, Transcendental field extensions, Group actions on varieties or schemes (quotients), Algebraic functions and function fields in algebraic geometry The variety of subfields of k(x)
| 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 \(x^n+y^m+1=0\) curve; function field; Jacobian; abelian variety; finite field; Mordell-Weil group; torsion; rank; \(L\)-function; Birch and Swinnerton-Dyer conjecture; Tate-Shafarevich group; Tamagawa number; endomorphism algebra; descent; height; Néron model; Kodaira-Spencer map; monodromy Research exposition (monographs, survey articles) pertaining to number theory, Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic functions and function fields in algebraic geometry Explicit arithmetic of Jacobians of generalized Legendre curves over 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 principle; function fields of \(p\)-adic curves Parimala, R.: A Hasse principle for quadratic forms over function fields. Bull. amer. Math. soc. (N.S.) 51, No. 3, 447-461 (2014) Quadratic forms over general fields, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields A Hasse principle for quadratic forms 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; holomorphic semisimple differentials; p- extensions of \({\mathbb{Z}}_ pfields\) of CM-type; p-class group G. Villa and M. Madan,Structure of semisimple differentials and p-class groups in \(\mathbb{Z}\) p -extensions. Manuscripta Mathematica57 (1987), 315--350. Cyclotomic extensions, Arithmetic theory of algebraic function fields, Iwasawa theory, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Algebraic functions and function fields in algebraic geometry Structure of semisimple differentials and p-class groups in \({\mathbb{Z}}_ p\)-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 \(x^n+y^m+1=0\) number of rational points; Deligne-Lusztig curves; function fields; large groups of automorphisms; Goppa codes HP Johan~P. Hansen and Jens~Peter Pedersen, \emph Automorphism groups of Ree type, Deligne-Lusztig curves and function fields, J. Reine Angew. Math. \textbf 440 (1993), 99--109. Algebraic functions and function fields in algebraic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic ground fields for curves, Curves over finite and local fields, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields Automorphism groups of Ree type, Deligne-Lusztig curves and 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 \(x^n+y^m+1=0\) Arithmetic theory of algebraic function fields, Cubic and quartic extensions, Units and factorization, Algebraic functions and function fields in algebraic geometry Purely cubic complex function fields with small units
| 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 \(x^n+y^m+1=0\) genus; prime divisor; discrete valuation ring of rank 1; algebraic function field of one variable; invariants Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On the genus of an algebraic 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 \(x^n+y^m+1=0\) global function fields; Artin-Schreier extensions; genus; rational places; towers; limit of towers; asymptotically good towers Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry A problem of Beelen, Garcia and Stichtenoth on an Artin-Schreier tower in characteristic 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 \(x^n+y^m+1=0\) abstract elliptic function fields Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On the theory of abstract elliptic 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 over finite fields; Kummer extensions; coding theory T. Hasegawa, An upper bound for the Garcia-Stichtenoth numbers of towers, Tokyo J. Math., 28 (2005), 471-481. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry, Algebraic coding theory; cryptography (number-theoretic aspects), Arithmetic codes An upper bound for the Garcia-Stichtenoth numbers of 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 \(x^n+y^m+1=0\) Hasse principle; integral quadratic forms; etale and flat cohomology; genus Quadratic forms over general fields, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Class numbers, class groups, discriminants, Arithmetic theory of algebraic function fields, Class groups and Picard groups of orders, Cohomology of arithmetic groups Between the genus and the \(\Gamma \)-genus of an integral quadratic \(\Gamma \)-form
| 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 \(x^n+y^m+1=0\) \(A\)-polynomials; elliptic function fields; Kloosterman sums; \(Q\)-transform Algebraic functions and function fields in algebraic geometry, Computational aspects of algebraic curves, Polynomials over finite fields, Arithmetic theory of polynomial rings over finite fields, Arithmetic theory of algebraic function fields Enumeration of a special class of irreducible polynomials in characteristic 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 \(x^n+y^m+1=0\) dihedral extensions; formula of Deuring-Shafarevich; Hasse-Witt invariants; number of ramified primes RÜCK, H.-G.: Hasse-Witt-Invariants and Dihedral Extensions, Math. Z., to appear Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves Hasse-Witt-invariants and dihedral 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 \(x^n+y^m+1=0\) simultaneous resolution; valuations; monomialization; local uniformization; function field DOI: 10.1006/jabr.1996.7014 Valuations and their generalizations for commutative rings, Arithmetic theory of algebraic function fields, Singularities in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Algebraic functions and function fields in algebraic geometry, Regular local rings Local weak simultaneous resolution for high rational ranks
| 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 \(x^n+y^m+1=0\) plane quartic curves; function field; Galois group K. Miura - H. Yoshihara, Field theory for function fields of plane quartic curves, J. Algebra, 226 (2000), pp. 283-294. Zbl0983.11067 MR1749889 Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Field theory for function fields of plane quartic 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 \(x^n+y^m+1=0\) points of finite order; best approximation in rings of algebraic functions; Jacobian Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Special algebraic curves and curves of low genus, Jacobians, Prym varieties Unités de certains sous-anneaux de corps de fonctions algébriques
| 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 theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry A theory of differentials in algebraic function fields with perfect field of constants.
| 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 \(x^n+y^m+1=0\) fields of moduli; fields of definition Dèbes, P., Douai, J.-C., Moret-Bailly, L.: Descent varieties for algebraic covers. J. fur die reine und angew. Math. 574, 51--78 (2004) Coverings in algebraic geometry, Arithmetic theory of algebraic function fields, Generalizations (algebraic spaces, stacks), Algebraic functions and function fields in algebraic geometry, Coverings of curves, fundamental group, Other nonalgebraically closed ground fields in algebraic geometry Descent varieties for algebraic covers
| 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; genus zero function fields; Ulm invariants; Leopoldt conjecture Brauer groups (algebraic aspects), Algebraic functions and function fields in algebraic geometry, Galois cohomology, Arithmetic theory of algebraic function fields Brauer groups of genus zero extensions of 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 \(x^n+y^m+1=0\) Arithmetic theory of algebraic function fields, Galois theory, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves Local-global Galois theory of arithmetic 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 \(x^n+y^m+1=0\) Puiseux series; rational curve; integer point; distribution Higher degree equations; Fermat's equation, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Algebraic functions and function fields in algebraic geometry On the distribution of integer points of rational 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 modules; injective modules; differentials; semisimple differentials; holomorphic differentials; modular representation Curves over finite and local fields, Integral representations related to algebraic numbers; Galois module structure of rings of integers, Arithmetic theory of algebraic function fields, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Algebraic functions and function fields in algebraic geometry Modular structure of semisimple differentials with prescribed poles
| 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 \(x^n+y^m+1=0\) functions fields; Gauss conjecture; zeta functions; Jacobian; hyperelliptic curves; finite fields Zeta and \(L\)-functions in characteristic \(p\), Class numbers, class groups, discriminants, Arithmetic theory of algebraic function fields, Quadratic extensions, Algebraic functions and function fields in algebraic geometry On some questions related to the Gauss conjecture for 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 \(x^n+y^m+1=0\) Aubry-Perret bound; finite field; Hasse-Weil bound; rational function Polynomials over finite fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry An application of the Hasse-Weil bound to rational functions 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 \(x^n+y^m+1=0\) gauged sheaves over global field; adeles; divisors; metrized line bundle; Haar measures; Riemann-Roch formula; Serre duality Adèle rings and groups, Global ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry The Riemann-Roch theorem and algebraic 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 \(x^n+y^m+1=0\) algebraic function field; rational function field; dihedral group; discriminant; zeta-function; divisor class number; ideal class number Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry, Zeta functions and \(L\)-functions of number fields On dihedral 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 \(x^n+y^m+1=0\) algebraic geometry codes; generalized algebraic geometry codes; minimum distance; floor bounds; bounds for codes Applications to coding theory and cryptography of arithmetic geometry, Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects), Algebraic functions and function fields in algebraic geometry Floor type bound for the minimum distance of generalized algebraic 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 \(x^n+y^m+1=0\) ramification of function field; reduction mod \(p\); elliptic curve; ordinary reduction; modular polynomial; complex multiplication Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Elliptic curves, Arithmetic ground fields for curves, Elliptic curves over global fields, Elliptic curves over local fields A note on elliptic curves with ordinary reduction
| 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 points of Drinfeld modules; arithmetic of function fields; class numbers; cyclotomic function fields; zeta-functions; Teichmüller characters; Artin conjecture; Artin L-series; p-adic measure; Main conjecture of Iwasawa theory; Frobenius; p-class groups; Bernoulli- Carlitz numbers Goss, D.: Analogies between global fields. Canad. math. Soc. conf. Proc. 7, 83-114 (1987) Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Fibonacci and Lucas numbers and polynomials and generalizations, Algebraic functions and function fields in algebraic geometry, Iwasawa theory, Cyclotomic extensions, Zeta functions and \(L\)-functions of number fields Analogies between global 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 \(x^n+y^m+1=0\) Galois subcovers; automorphisms Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry A new family of maximal 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 \(x^n+y^m+1=0\) Hasse--Witt map; Hasse--Witt invariant; Hasse--Witt matrix; Witt vectors; holomorphic differentials; Cartier operator; maximal abelian extension Maldonado Ramírez, Cyclic p-extensions of function fields with null Hasse-Witt map, Int. Math. Forum 2 (49-52) pp 2463-- (2007) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Cyclic \(p\)-extensions of function fields with null Hasse-Witt map
| 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 Hasse, H., Zur theorie der abstrakten elliptischen funktionenkörper. I. die struktur der gruppe der divisorenklassen endlicher ordnung, J. Reine Angew. Math., 1936, 175, 55-62, (1936) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Zur Theorie der abstrakten elliptischen Funktionenkörper. I: Die Struktur der Gruppe der Divisorenklassen endlicher Ordnung
| 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 \(x^n+y^m+1=0\) fields of real algebraic functions; reduced Whitehead group; Hasse principle; norm mapping Class field theory, Algebraic functions and function fields in algebraic geometry, \(K\)-theory of global fields, Arithmetic theory of algebraic function fields, Quaternion and other division algebras: arithmetic, zeta functions, Finite-dimensional division rings, Grothendieck groups, \(K\)-theory, etc. Norms in fields of real algebraic functions, and the reduced Whitehead 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 \(x^n+y^m+1=0\) function fields; \(S\)-class groups; units; regulators; \(L\)-functions; Galois module structure Popescu C.D.: Gras-type conjectures for function fields. Compositio Mathematica 118, 263--290 (1999) Arithmetic theory of algebraic function fields, Integral representations related to algebraic numbers; Galois module structure of rings of integers, Zeta functions and \(L\)-functions of number fields, Algebraic functions and function fields in algebraic geometry Gras-type conjectures for 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 \(x^n+y^m+1=0\) singular primes in function fields; extension of field of constants; genus Stöhr, K-O, On singular primes in function fields, Arch. Math., 50, 156-163, (1988) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On singular primes 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 \(x^n+y^m+1=0\) global function field; arithmetic equivalence; Gassmann equivalence; Weil zeta function; Goss zeta function J NUMBER THEORY 130 pp 1000-- (2010) Zeta and \(L\)-functions in characteristic \(p\), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Arithmetic equivalence for function fields, the Goss zeta function and a generalisation
| 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 \(x^n+y^m+1=0\) genus; rational places; existence of algebraic function fields; Abelian extensions; different [F-P-S] G. Frey, M. Perret and H. Stichtenoth,On the different of Abelian extensions of global fields, inCoding Theory and Algebraic Geometry (H. Stichtenoth and M. Tsfasman, eds.), Proceedings AGCT3, Luminy June 1991, Lecture Notes in Mathematics1518, Springer, Heidelberg, 1992, pp. 26--32. Arithmetic theory of algebraic function fields, Class field theory, Other abelian and metabelian extensions, Algebraic functions and function fields in algebraic geometry On the different of Abelian extensions of global 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 map; Artin-Schreier extensions; semisimple differentials; Cartier operator Rzedowski-Calderón, Martha; Villa-Salvador, Gabriel, Function field extensions with null Hasse-Witt map, Int. Math. J., 2, 4, 361-371, (2002), MR 1891121 (2003d:11172) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves Function field extensions with null Hasse-Witt map.
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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 \(x^n+y^m+1=0\) Brauer group; function field of the projective line Mestre, J.F. 1994.Annulation, par changement de variable, d'éléments de Br2(k(x)) ayant quatre pôles, SÉrie I Vol. 319, 529--532. Paris: C. R. Acad. Sci. Brauer groups of schemes, Arithmetic theory of algebraic function fields, Galois cohomology, Algebraic functions and function fields in algebraic geometry Base change killing of elements of \(\text{Br}_ 2 (k(x))\) with four poles
| 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 \(x^n+y^m+1=0\) good towers; graphs Beelen, Peter; Garcia, Arnaldo; Stichtenoth, Henning, On towers of function fields over finite fields.Arithmetic, geometry and coding theory (AGCT 2003), Sémin. Congr. 11, 1-20, (2005), Soc. Math. France, Paris Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Curves over finite and local fields, Rational points On towers 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 fields; divisors Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On divisors in the field of algebraic functions 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 \(x^n+y^m+1=0\) distribution of ideal class groups of imaginary quadratic fields; distribution of class groups of hyperelliptic function fields; \(\ell\)-adic Tate module; equidistribution conjecture; Cohen-Lenstra principle Friedman, Eduardo; Washington, Lawrence C., On the distribution of divisor class groups of curves over a finite field.Théorie des nombres, Quebec, PQ, 1987, 227\textendash 239 pp., (1989), de Gruyter, Berlin Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry On the distribution of divisor class groups of curves 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 \(x^n+y^m+1=0\) meromorphisms; elliptic function field Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry The meromorphisms of an elliptic 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 \(x^n+y^m+1=0\) cyclotomic function fields; arithmetic of Witt vectors; Artin-Schreier extensions; maximal abelian extension; ramification theory Cyclotomic function fields (class groups, Bernoulli objects, etc.), Cyclotomic extensions, Class field theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Analog of the Kronecker-Weber theorem 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 \(x^n+y^m+1=0\) Stickelberger element; Galois module structure; Gras conjecture; Drinfeld modules; Herbrand criterion; crystalline cohomology; zeta-functions for function fields over finite fields; L-series; Teichmüller character; characteristic polynomial of the Frobenius; p-adic Tate-module; p-class groups; cyclotomic function fields; 1-unit root Goss, D., Sinnott, W.: Class-groups of function fields. Duke Math. J. 52(2), 507--516 (1985). http://www.ams.org/mathscinet-getitem?mr=792185 Arithmetic theory of algebraic function fields, \(p\)-adic cohomology, crystalline cohomology, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Iwasawa theory Class-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 \(x^n+y^m+1=0\) towers of function fields; genus; number of places [HST]F. Hess, H. Stichtenoth and S. Tutdere, On invariants of towers of function fields over finite fields, J. Algebra Appl. 12 (2013), no. 4, #1250190. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On invariants of towers 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 \(x^n+y^m+1=0\) hyperelliptic curves; hyperelliptic function fields; algebraic function field; holomorphic differentials; Hasse-Witt matrix; Cartier operator Kodama,T.,Washio,T.: Hasse-Witt matrices of hyperelliptic function fields. Sci. Bull. Fac. Educ. Nagasaki Univ.37, 9-15 (1986) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials Hasse-Witt matrices 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 \(x^n+y^m+1=0\) valued function fields; genus change; algebraic function field; reduction of constants; rigid analytic geometry; non-discrete valuation; defect; ramification index Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Non-Archimedean valued fields, Arithmetic ground fields for surfaces or higher-dimensional varieties Genre des corps de fonctions valués après Deuring, Lamprecht et Mathieu. (Genus of valued function fields after Deuring, Lamprecht and Mathieu)
| 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 \(x^n+y^m+1=0\) places separably generated in algebraic function fields Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry Singular places 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 \(x^n+y^m+1=0\) Tate-Poitou theorem; duality; finite groups Douai, J. C.: Le théorème de Tate-poitou pour LES corps de fonctions des courbes définies sur LES corps locaux de dimension N. J. algebra 125, 181-196 (1989) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Le théorème de Tate-Poitou pour les corps de fonctions des courbes définies sur les corps locaux de dimension N. (The Tate-Poitou theorem for function fields of curves defined over local fields of dimension N)
| 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 \(x^n+y^m+1=0\) congruence subgroups; infinite rank free quotients; algebraic function fields A. W. Mason, Free quotients of congruence subgroups of the Serre groups and unipotent matrices, Comm. Algebra 27 (1999), no. 1, 335 -- 356. Unimodular groups, congruence subgroups (group-theoretic aspects), Subgroup theorems; subgroup growth, Algebraic functions and function fields in algebraic geometry, Linear algebraic groups over arbitrary fields, Arithmetic theory of algebraic function fields, Structure of modular groups and generalizations; arithmetic groups Free quotients of congruence subgroups of the Serre groups and unipotent matrices
| 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 algorithm; full partial fraction expansion; rational function; algebraic closure Bronstein, M., Salvy, B.: Full partial fraction decomposition of rational functions. In: ISSAC '93: Proceedings of the 1993 International Symposium on Symbolic and Algebraic Computation, pp. 157--160. ACM, New York, NY, USA (1993) Symbolic computation and algebraic computation, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields Full partial fraction decomposition of 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 \(x^n+y^m+1=0\) function fields; Kronecker; Dedekind; Weber; Hensel; Noether; Dedekind rings [1999] ??Die Entdeckung der Analogie zwischen Zahl- und Funktionenkörper: der Ursprung der ?Dedekind-Ringe,?? Jahresbericht der DMV 101 (1999): 116-134. History of number theory, Arithmetic theory of algebraic function fields, History of mathematics in the 19th century, History of mathematics in the 20th century, Algebraic number theory: global fields, Dedekind, Prüfer, Krull and Mori rings and their generalizations, History of algebraic geometry, Algebraic functions and function fields in algebraic geometry On the discovery of the analogy between number and function fields: The origin of Dedekind rings
| 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. Rosen, \textit{S}-units and \textit{S}-class group in algebraic function fields, J. Algebra 26 (1973), 98-108. Arithmetic theory of algebraic function fields, Units and factorization, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry, Global ground fields in algebraic geometry \(S\)-units and \(S\)-class group in 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 \(x^n+y^m+1=0\) Riemann-Roch theorem; function fields; Fourier transforms; adelic Poisson summation formula Li, X-J, A note on the Riemann-Roch theorem for function fields, No. 2, 567-570, (1996), Basel Arithmetic theory of algebraic function fields, Riemann-Roch theorems, Algebraic functions and function fields in algebraic geometry A note on the Riemann-Roch theorem for 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 \(x^n+y^m+1=0\) Brauer groups; division algebras; central simple algebras; symbol algebras; cyclic algebras; cubic curves; ramification divisors; rational function fields [Fo] T. Ford,Division algebras that ramify only along a singular plane cubic curve, New York Journal of Mathematics1 (1995), 178--183, http://nyjm.albany.edu:8000/j/v1/ford.html. Finite-dimensional division rings, Arithmetic theory of algebraic function fields, Quaternion and other division algebras: arithmetic, zeta functions, Skew fields, division rings, Algebraic functions and function fields in algebraic geometry Division algebras that ramify only along a singular plane cubic curve
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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 \(x^n+y^m+1=0\) Artin-Schreier type extensions; function fields; character sums; cyclic codes; trace codes; Wolfmann's bound Güneri C., Özbudak F.: Artin--Schreier extensions and their applications. In: Garcia, A., Stichtenoth, H.(eds) Topics in Geometry, Coding Theory and Cryptography, Algebra and Applications, vol. 6, pp. 105--133. Springer, Dordrecht (2007) Arithmetic theory of algebraic function fields, Weyl sums, Algebraic functions and function fields in algebraic geometry, Cyclic codes, Geometric methods (including applications of algebraic geometry) applied to coding theory, Other abelian and metabelian extensions Artin-Schreier extensions 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 \(x^n+y^m+1=0\) real quadratic function fields; Ankeny-Artin-Chowla theorem; function fields; fundamental unit Yu, J.; Yu, J. -K.: A note on a geometric analogue of ankeny--Artin--chowla's conjecture. (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Units and factorization A note on a geometric analogue of Ankeny-Artin-Chowla's conjecture
| 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; ramification; Abhyankar's Lemma Anbar, N.; Stichtenoth, H.; Tutdere, S., On ramification in the compositum of function fields, Bull. Braz. Math. Soc. (N.S.), 40, 4, 539-552, (2009) Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields On ramification in the compositum 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 \(x^n+y^m+1=0\) Hasse-Witt matrix; hyperelliptic curves; hyperelliptic function fields; algebraic function field; class number; supersingular T. Washio and T. Kodama: A note on a supersingular function field. Sci. Bull. Fac. Ed. Nagasaki Univ., 37, 17-21 (1986). Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry A note on a supersingular 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 \(x^n+y^m+1=0\) Geyer, W. D.; Martens, G.: Überlagerungen berandeter kleinscher, Flächen. math. Ann. 228, 101-111 (1977) Coverings of curves, fundamental group, Algebraic functions and function fields in algebraic geometry, Global ground fields in algebraic geometry, Separable extensions, Galois theory, Arithmetic theory of algebraic function fields Überlagerungen berandeter Kleinscher Flächen
| 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 \(x^n+y^m+1=0\) Gauss' genus theory; class number formula for tori Algebraic number theory, (1986), CasselsJ. W. S.J. W. S., London Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Toric varieties, Newton polyhedra, Okounkov bodies, Galois theory Algebraic groups and number theory
| 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 \(x^n+y^m+1=0\) Coverings of curves, fundamental group, Algebraic functions and function fields in algebraic geometry, Modular and automorphic functions, Arithmetic theory of algebraic function fields On \((\infty\times p)\)-adic coverings of curves (the simplest example)
| 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 \(x^n+y^m+1=0\) Gauss' genus theory; class number formula for tori Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Toric varieties, Newton polyhedra, Okounkov bodies, Galois theory Algebraic groups and number theory
| 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 \(x^n+y^m+1=0\) Carlitz module; Artin's conjecture; function fields Cyclotomic function fields (class groups, Bernoulli objects, etc.), Well-distributed sequences and other variations, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On extending Artin's conjecture to composite moduli 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 function fields; Poincaré residue; differential form; rank n discrete valuation Kawahara, Y., Uchibori, T.: On residues of differential forms in algebraic function fields of several variables. TRU Math.21, 173--180 (1985) Arithmetic theory of algebraic function fields, Morphisms of commutative rings, Transcendental field extensions, Valued fields, Algebraic functions and function fields in algebraic geometry, Relevant commutative algebra On residues of differential forms in algebraic function fields of several 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 \(x^n+y^m+1=0\) endomorphism ring; stable reduction; good reduction; Tate parametrization; supersingular Drinfeld modules; Hasse invariant Gekeler E.-U.: Zur Arithmetik von Drinfeld-Moduln. Math. Ann. 262, 167--182 (1983) Drinfel'd modules; higher-dimensional motives, etc., Arithmetic ground fields for abelian varieties, Global ground fields in algebraic geometry, Formal groups, \(p\)-divisible groups, Algebraic functions and function fields in algebraic geometry, Complex multiplication and abelian varieties, Complex multiplication and moduli of abelian varieties, Arithmetic theory of algebraic function fields Zur Arithmetik von Drinfeld-Moduln
| 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; Pólya ring; integer valued polynomials F. J. Van Der Linden, Integer valued polynomials over function fields, \(Nederl. Akad. Wetensch. Indag. Math.\)50 (1988), 293-308. Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Polynomials over finite fields Integer valued polynomials 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 \(x^n+y^m+1=0\) Galois groups of algebraic curve Algebraic functions and function fields in algebraic geometry, Galois theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields On the Galois group corresponding to the formula of Grant
| 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 \(x^n+y^m+1=0\) inverse problem of Galois theory; Fischer-Griess monster as Galois group over \({\mathbb{Q}}\); finite simple groups; fundamental group; rigid simple groups; cyclotomic field; discrete subgroups of \(PSL_ 2({\mathbb{R}})\); congruence subgroup; modular curve; Puiseux-series; group of covering transformations; compact Riemann surface; algebraic function field; ramification points; cusps; lectures Galois theory, Simple groups: sporadic groups, Representations of groups as automorphism groups of algebraic systems, Arithmetic theory of algebraic function fields, Simple groups: alternating groups and groups of Lie type, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Compact Riemann surfaces and uniformization, Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory Some finite groups which appear as Gal L/K, where \(K\subseteq {\mathbb{Q}}(\mu _ n)\)
| 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 \(x^n+y^m+1=0\) inverse Galois problem; Galois extension of function field; Riemann- Hurwitz formula; genus; mock covers of curves DOI: 10.2307/2159335 Algebraic functions and function fields in algebraic geometry, Inverse Galois theory, Birational automorphisms, Cremona group and generalizations, Automorphisms of curves, Arithmetic theory of algebraic function fields, Curves in algebraic geometry The automorphism group 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 \(x^n+y^m+1=0\) error-correcting codes; curves over finite fields Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects), Algebraic functions and function fields in algebraic geometry Upper and lower bounds for \(A(q)\)
| 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 \(x^n+y^m+1=0\) geometric theory of algebraic functions of one variable; Riemann-Roch theorem; algebraically perfect fields W. L. Chow, Die geometrische Theorie der algebraischen Funktionen für beliebige vollkommene Körper, Math. Ann. (1937) pp. 656-682. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Die geometrische Theorie der algebraischen Funktionen für beliebige vollkommene Körper
| 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; automorphisms of rational function field; Lüroth extensions; \(PSL({\mathbb{F}}_ q)\); holomorphic differentials; different; genus Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry The genera of \(PSL({\mathbb{F}}_ q)\)-Lüroth coverings
| 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 cover; Artin-Schreier cover; maximal curves Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry Fibre products of Kummer and 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 \(x^n+y^m+1=0\) hyperelliptic function field; quasi-periodic continued fraction expansions; quasi-periodicity; periodicity Arithmetic theory of algebraic function fields, Continued fractions and generalizations, Algebraic functions and function fields in algebraic geometry Periodicity of continued fractions in 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 \(x^n+y^m+1=0\) finite field; towers of algebraic function fields Arithmetic theory of algebraic function fields, Class field theory, Algebraic functions and function fields in algebraic geometry, Rational points A note on towers 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 \(x^n+y^m+1=0\) Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry, Zeta functions and \(L\)-functions of number fields Errata in ``On dihedral 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 \(x^n+y^m+1=0\) inverse problem of Galois theory; Fischer-Griess monster as Galois group over \(\mathbb{Q}\); finite simple groups; fundamental group; rigid simple groups; cyclotomic field; discrete subgroups of \(PSL_2(\mathbb{R})\); congruence subgroup; modular curve; Puiseux series; group of covering transformations; compact Riemann surface; algebraic function field; ramification points; cusps J. Thompson , Some finite groups which appear as Gal (L/K) where K \subset Q(\mu n) , J. Alg. 89 (1984) 437-499. Galois theory, Simple groups: sporadic groups, Representations of groups as automorphism groups of algebraic systems, Arithmetic theory of algebraic function fields, Simple groups: alternating groups and groups of Lie type, Unimodular groups, congruence subgroups (group-theoretic aspects), Finite automorphism groups of algebraic, geometric, or combinatorial structures, Compact Riemann surfaces and uniformization, Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory Some finite groups which appear as \(\mathrm{Gal } L/K\), where \(K\subseteq \mathbb{Q}(\mu_n)\)
| 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; no movable singularity; strongly normal extension; weakly normal Differential algebra, Arithmetic ground fields for curves, Group actions on varieties or schemes (quotients), \(p\)-adic differential equations, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields Movable singularities and differential Galois theory
| 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 \(x^n+y^m+1=0\) invariant field of automorphism group; rational function field; rationality problem Rational and unirational varieties, Group actions on varieties or schemes (quotients), Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Actions of groups on commutative rings; invariant theory Finite group actions on rational 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; curves of genus greater than 1; finite number of points defined over the ground field Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic theory of algebraic function fields, Rational points Diophantine 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 \(x^n+y^m+1=0\) \((t,s)\)-sequences; \((t,m,s)\)-nets; survey; orthogonal latin squares; orthogonal array; rational points; algebraic-geometric codes; bounds; curves over a finite field Harald Niederreiter, Nets, (\?,\?)-sequences, and algebraic curves over finite fields with many rational points, Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998), 1998, pp. 377 -- 386. Pseudo-random numbers; Monte Carlo methods, Curves over finite and local fields, Orthogonal arrays, Latin squares, Room squares, Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects), Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Bounds on codes Nets, \((t,s)\)-sequences, and algebraic curves over finite fields with many rational points
| 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 \(x^n+y^m+1=0\) separable algebraic function field; s-subfield; unique maximal s- subfield; inequality of Castelnuovo; hyperelliptic function field H. Stichtenoth, s-Erweiterungen algebraischer Funktionenkörper. Arch. Math. 43, 27--31 (1984). Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Coverings of curves, fundamental group s-Erweiterungen 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 \(x^n+y^m+1=0\) algebraic functions of one variable; algebraic function fields; arbitrary field of constants Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Fields of algebraic functions of one variable over an arbitrary field of constants
| 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 \(x^n+y^m+1=0\) defect of the valued function fields; genus; ramification index Michel Matignon, Genre et genre résiduel des corps de fonctions valués, Manuscripta Math. 58 (1987), no. 1-2, 179 -- 214 (French, with English summary). Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Ramification problems in algebraic geometry, Valued fields Genre et genre residuel des corps de fonctions valués. (Genus and residual genus of 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 \(x^n+y^m+1=0\) ramification index; Puiseux expansions; algebraic function; algorithm David Lee Hilliker, An algorithm for computing the values of the ramification index in the Puiseux series expansions of an algebraic function, Pacific J. Math. 118 (1985), no. 2, 427 -- 435. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry An algorithm for computing the values of the ramification index in the Puiseux series expansions 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 \(x^n+y^m+1=0\) densities of discriminants of cubic fields; 3-class-number of quadratic fields; binary cubic forms; adelization; zeta-functions; function field; Dedekind's zeta-function Iwasawa theory, Arithmetic theory of algebraic function fields, Quadratic forms over global rings and fields, Density theorems, Asymptotic results on counting functions for algebraic and topological structures, Cubic and quartic extensions, Global ground fields in algebraic geometry, Zeta functions and \(L\)-functions of number fields, Algebraic functions and function fields in algebraic geometry Density of discriminants of cubic 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 \(x^n+y^m+1=0\) finite fields; towers of function fields; congruence zeta functions DOI: 10.3836/tjm/1202136690 Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry A note on optimal towers 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 \(x^n+y^m+1=0\) transfer principle; absolute Galois group of the rational function field; real closed field; Tarski principle L. van den Dries and P. Ribenboim, ''An application of Tarski's principle to absolute Galois groups of function fields,'' Ann. Pure Appl. Log., 33, 83--107 (1987). 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 \(x^n+y^m+1=0\) curves over finite fields; error-correction codes; function field; genus Lewittes J.: Places of degree one in function fields over finite fields. J. Pure Appl. Algebra. 69(2), 177--183 (1990) Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory Places of degree one in 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 \(x^n+y^m+1=0\) unramified extensions; function fields over finite fields Y. Ihara , On unramified extensions of function fields over finite fields . In Y. IHARA, editor, Galois Groups and Their Representations , volume 2 of Adv. Studies in Pure Math. 89 - 97 . North-Holland , 1983 . MR 732464 | Zbl 0542.14011 Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On unramified extensions 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 \(x^n+y^m+1=0\) Galois theory; Galois group; full automorphism group; Galois extension; inverse Galois problem; separably generated extension; solvable group; algebraic function field; rational function field; ramified; perfect field; genus; place; Castelnuovo-Severi inequality Inverse Galois theory, Arithmetic theory of algebraic function fields, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Representations of groups as automorphism groups of algebraic systems, Algebraic functions and function fields in algebraic geometry Finite groups as Galois groups of function fields with infinite field of constants
| 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 function fields; rational places; genus of a function field; automorphisms of function fields; \(p\)-rank Arithmetic theory of algebraic function fields, Curves over finite and local fields, Applications to coding theory and cryptography of arithmetic geometry, Algebraic functions and function fields in algebraic geometry Asymptotically good towers of function fields with small \(p\)-rank
| 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 \(x^n+y^m+1=0\) reduced Whitehead groups; Tannaka-Artin problem; patching; \(\mathrm{SK}_1\); function fields of \(p\)-adic curves Finite-dimensional division rings, Brauer groups (algebraic aspects), Arithmetic theory of algebraic function fields, Arithmetic ground fields for curves, Algebraic functions and function fields in algebraic geometry Reduced Whitehead groups of prime exponent algebras over \(p\)-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 \(x^n+y^m+1=0\) theorem of Deuring and Shafarevich; algebraic function field; modular representation; rank of class group; ramification index R. Gold andM. Madan, An application of a Theorem of Deuring and Safarevic. Math. Z.191, 247-251 (1986). Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry An application of a theorem of Deuring and Šafarevič
| 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 \(x^n+y^m+1=0\) 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 Correction to: ``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 \(x^n+y^m+1=0\) algebraic function fields of genus one; real-closed field; J-invariant Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Real algebraic and real-analytic geometry, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) An isomorphism theorem for algebraic function fields of genus one over real-closed 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; higher differential quotients Hasse, Helmut; Schmidt, Friedrich K., Noch eine begründung der theorie der höheren differentialquotienten in einem algebraischen funktionenkörper einer unbestimmten. (nach einer brieflichen mitteilung von F.K.Schmidt in jena), Journal für die reine und angewandte Mathematik, 177, 215-223, (1937) Arithmetic theory of algebraic function fields, Differential algebra, Algebraic functions and function fields in algebraic geometry Noch eine Begründung der Theorie der höheren Differentialquotienten in einem algebraischen Funktionenkörper einer Unbestimmten
| 0 |
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