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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 \(x^n+y^m+1=0\) elliptic curve; rank Koh-ichi Nagao, An example of elliptic curve over \?(\?) with rank \ge 13, Proc. Japan Acad. Ser. A Math. Sci. 70 (1994), no. 5, 152 -- 153. Elliptic curves, Arithmetic ground fields for curves, Algebraic functions and function fields in algebraic geometry, Elliptic curves over global fields An example of elliptic curve over \(\mathbb{Q}(T)\) with rank \(\geq 13\)
| 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 curves; elliptic sequences; continued fractions; singular case; periodicity; function field Van Der Poorten, A.: Elliptic curves and continued fractions. Journal of integer sequences 8, No. 2, 1-19 (2005) Continued fractions, Elliptic curves over global fields, Algebraic functions and function fields in algebraic geometry, Elliptic curves, Special sequences and polynomials, Special algebraic curves and curves of low genus Elliptic curves and continued fractions
| 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 \(x^n+y^m+1=0\) multiplication algorithm; bilinear complexity; elliptic function field; interpolation on algebraic curve; finite field Ballet, Stéphane; Bonnecaze, Alexis; Tukumuli, Mila, On the construction of elliptic Chudnovsky-type algorithms for multiplication in large extensions of finite fields, J. Algebra Appl., 0219-4988, 15, 1, 1650005, 26 pp., (2016) Number-theoretic algorithms; complexity, Structure theory for finite fields and commutative rings (number-theoretic aspects), Arithmetic theory of algebraic function fields, Elliptic curves, Cryptography On the construction of elliptic Chudnovsky-type algorithms for multiplication in large extensions of 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 action; Mordell-Weil group doi:10.4064/aa108-1-3 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves Parametrization of low-degree points on a Fermat 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 \(x^n+y^m+1=0\) rational points; descent obstruction; covering; twist; torsor under finite group scheme; Brauer-Manin obstruction M. Stoll, ''Finite descent obstructions and rational points on curves,'' Algebra Number Theory, vol. 1, iss. 4, pp. 349-391, 2007. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Abelian varieties of dimension \(> 1\), Coverings of curves, fundamental group Finite descent obstructions and rational points on 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 \(x^n+y^m+1=0\) anabelian geometry; valuations; section conjecture Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Galois theory, Arithmetic theory of algebraic function fields, Rationality questions in algebraic geometry, Higher symbols, Milnor \(K\)-theory Homomorphisms of multiplicative groups of fields preserving algebraic dependence
| 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 \(x^n+y^m+1=0\) reductive algebraic groups over local fields; Bruhat-Tits buildings Linear algebraic groups over local fields and their integers, Algebraic functions and function fields in algebraic geometry, Groups acting on trees, Groups with a \(BN\)-pair; buildings On the structure of the fundamental domain of arithmetic subgroups of the symplectic group 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 \(x^n+y^m+1=0\) curves over finite fields with many rational points; asymptotic lower bounds; class field towers; degree-2 covering of curves Applications to coding theory and cryptography of arithmetic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Curves over finite and local fields, Arithmetic theory of algebraic function fields The zeta functions of two Garcia-Stichtenoth 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 \(x^n+y^m+1=0\) field extension; genus; Riemann-Roch theorem; algebraic function fields; different divisor; differentials Differential algebra, Field extensions, Algebraic functions and function fields in algebraic geometry On the notion of a differential in the theory of algebraic functions with arbitrary constant 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 group; Galois closure; automorphism group; plane curve Algebraic functions and function fields in algebraic geometry, Automorphisms of curves, Plane and space curves Algebraic curves admitting the same Galois closure for two projections
| 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 \(x^n+y^m+1=0\) Picard number; Néron-Severi group; K3-surfaces Picard groups, \(K3\) surfaces and Enriques surfaces, Elliptic curves, Arithmetic theory of algebraic function fields On the rank of elliptic curves over \(\mathbb{Q}(t)\) arising from K3 surfaces
| 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 with only one branch at infinity; characteristic \(p\); Newton polygons Reguera López, A.: Semigroups and clusters at infinitiy. Algebraic geometry and singularities (La Rábida, 1991), Progr. Math., vol. 134, pp. 339-374. Birkhäuser, Basel (1996) Algebraic functions and function fields in algebraic geometry, Ramification problems in algebraic geometry Semigroups and clusters at infinity
| 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 of genus zero; \(S\)-integral points; Riemann-Roch basis Curves of arbitrary genus or genus \(\ne 1\) over global fields, Higher degree equations; Fermat's equation, Global ground fields in algebraic geometry, Arithmetic ground fields for curves An upper bound for the number of \(S\)-integral points on curves of genus zero
| 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 \(x^n+y^m+1=0\) The arithmetic theory of algebraic functions Algebraic functions and function fields in algebraic geometry On the reduction of algebraic systems to canonical 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 \(x^n+y^m+1=0\) Blum, A., Stuhler, U.: Drinfeld modules and elliptic sheaves. In: Kumar, S., Laumon, G., Stuhler, U., Narasimhan, M. S. (eds.) Vector Bundles on Curves: New Directions. Lecture Notes in Mathematics, vol. 1649, pp. 110--188. Springer-Verlag, Berlin (1991) Drinfel'd modules; higher-dimensional motives, etc., Finite ground fields in algebraic geometry, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions, Arithmetic theory of algebraic function fields Drinfeld modules and elliptic sheaves
| 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; plane curves of genus one; exceptional points Nagell, T.: [3] ''Les points exceptionnels sur les cubiques planes du premier genre'', II, ibid. Nova Acta Reg. Soc. Sci. Upsaliensis, Ser. IV, 14, 1946, No. 3. Algebraic functions and function fields in algebraic geometry, Special algebraic curves and curves of low genus Les points exceptionnels sur les cubiques planes du premier genre
| 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 \(x^n+y^m+1=0\) Diophantine equation of degree seven; nonabelian descent Higher degree equations; Fermat's equation, Abelian varieties of dimension \(> 1\), Arithmetic aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points The equation \(x^2+y^3=z^7\)
| 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 \(x^n+y^m+1=0\) Arakelov theory; singular surfaces; algebraic curves; moduli spaces; moduli stacks; enumerative geometry of moduli spaces; Deligne pairing L. Weng, \(\Omega\) -admissible theory, II: Deligne pairings over moduli spaces of punctured Riemann surfaces, Math. Ann. 320 (2001), 239--283. Arithmetic varieties and schemes; Arakelov theory; heights, Families, moduli of curves (analytic), Riemann surfaces; Weierstrass points; gap sequences, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Generalizations (algebraic spaces, stacks) \(\Omega\)-admissible theory. II: Deligne pairings over moduli spaces of punctured Riemann surfaces
| 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 \(x^n+y^m+1=0\) Fermat curve; Jacobian variety; elliptic curve; canonical height Dąbrowski, A.; Jędrzejak, T.: Ranks in families of Jacobian varieties of twisted Fermat curves, Canad. math. Bull. 53, 58-63 (2010) Abelian varieties of dimension \(> 1\), Elliptic curves over global fields, Heights, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus, Arithmetic ground fields for abelian varieties Ranks in families of Jacobian varieties of twisted Fermat 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 \(x^n+y^m+1=0\) periodic points; algebraic function; class number formula; modular function; ring class fields Algebraic functions and function fields in algebraic geometry, Higher degree equations; Fermat's equation, Elliptic curves over local fields, Complex multiplication and moduli of abelian varieties Periodic points of algebraic functions and Deuring's class number formula
| 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 \(x^n+y^m+1=0\) Combinatorial codes, Algebraic coding theory; cryptography (number-theoretic aspects), Algebraic functions and function fields in algebraic geometry, Bounds on codes A construction of permutation codes from rational function fields and improvement to the Gilbert-Varshamov bound
| 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 2 curves; isogenies; split Jacobians; elliptic curves genus 2 curves; isogenies; split Jacobians; elliptic curves Bruin, N; Doerksen, K, The arithmetic of genus two curves with \((4,4)\)-split Jacobians, Can. J. Math., 63, 992-1021, (2011) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Period matrices, variation of Hodge structure; degenerations The arithmetic of genus two curves with \((4,4)\)-split Jacobians
| 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 \(x^n+y^m+1=0\) Dèbes, Finiteness results in descent theory, J. London Math. Soc. 68 pp 52-- (2003) Global ground fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields Finiteness results in descent 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 \(x^n+y^m+1=0\) rigid analytic geometry; formal methods; automorphisms of curves; Mumford curves; Schottky groups G. CORNELISSEN - F. KATO, Equivariant deformation of Mumford curves and of ordinary curves in positive characteristic, Duke Math. J., 116 (2003), pp. 431-470. Zbl1092.14032 MR1958094 Rigid analytic geometry, Formal methods and deformations in algebraic geometry, Automorphisms of curves, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields Equivariant deformation of Mumford curves and of ordinary curves 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 \(x^n+y^m+1=0\) genus-2 curves; torsion; modular curves; Jacobians; rational point of order 11 Bernard, N.; Leprévost, F.; Pohst, M., Jacobians of genus-2 curves with a rational point of order 11, Exp. Math., 18, 1, 65-70, (2009) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Global ground fields in algebraic geometry, Jacobians, Prym varieties Jacobians of genus-2 curves with a rational point of order 11
| 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 \(x^n+y^m+1=0\) Noether's theorem; fundamental theorem; theory of algebraic functions Algebraic functions and function fields in algebraic geometry On the fundamental theorem of the theory 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 \(x^n+y^m+1=0\) periodic points; algebraic functions; 5-adic field; ring class fields; Rogers-Ramanujan continued fraction Higher degree equations; Fermat's equation, Elliptic curves over local fields, Complex multiplication and moduli of abelian varieties, Algebraic functions and function fields in algebraic geometry Solutions of Diophantine equations as periodic points of \(p\)-adic algebraic functions. II: The Rogers-Ramanujan continued fraction
| 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; Hurwitz genus formula; nilpotent group; positive characteristic Algebraic functions and function fields in algebraic geometry, Automorphisms of curves On nilpotent automorphism 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 \(x^n+y^m+1=0\) Morton-Silverman conjecture; uniform boundedness; periodic points Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps, Arithmetic varieties and schemes; Arakelov theory; heights Uniform bounds for periods of endomorphisms of varieties
| 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 point; hyperelliptic curve; height Lee, J.; Murty, M. Ram, An application of Mumford's gap principle, J. Number Theory, 105, 333-343, (2004) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves over global fields, Heights, Rational points An application of Mumford's gap principle.
| 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 \(x^n+y^m+1=0\) External book reviews, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Zeta functions and \(L\)-functions of number fields, Arithmetic theory of algebraic function fields, Zeta functions and \(L\)-functions Book review of: M. van Frankenhuijsen, The Riemann hypothesis for function fields. Frobenius flow and shift operators
| 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 and function fields in algebraic geometry, Low codimension problems in algebraic geometry, Surfaces and higher-dimensional varieties Lifting problem in codimension 2 and initial ideals
| 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 \(x^n+y^m+1=0\) Beilinson-Bloch conjecture; degree-zero cycles modulo rational equivalence; Albanese map Schoen, C., Zero cycles modulo rational equivalence for some varieties over fields of transcendence degree one, Proc. Symp. Pure Math. 46 (1987), part 2, pp. 463-473. Algebraic cycles, (Equivariant) Chow groups and rings; motives, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic theory of algebraic function fields Zero cycles modulo rational equivalence for some varieties over fields of transcendence degree 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 \(x^n+y^m+1=0\) approximation; function field; transfer lemma; algebraic independence; Hilbert function DOI: 10.1142/S1793042111004502 Approximation in non-Archimedean valuations, Algebraic functions and function fields in algebraic geometry Functional approximations of curves in projective space
| 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 \(x^n+y^m+1=0\) two dimensional global fields; algebraic function field in one; variable over algebraic number field; Galois cohomology group; \(H^ 3\); Hasse principles; local-global principles; reduced norms; division algebras; quadratic forms; sum of squares K.~Kato, {A {H}asse principle for two dimensional global fields. With an appendix by {J}.-{L} {C}olliot-{T}hélène.}, J. Reine Angew. Math. {366} (1986), 142--180. DOI 10.1515/crll.1986.366.142; zbl 0576.12012; MR0833016 Galois cohomology, Brauer groups of schemes, Quadratic forms over global rings and fields, Galois cohomology, Quaternion and other division algebras: arithmetic, zeta functions, Waring's problem and variants, Arithmetic theory of algebraic function fields A Hasse principle for two dimensional global fields. Appendix by Jean-Louis Colliot-Thélène
| 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; automorphism groups; \(p\)-rank Automorphisms of curves, Algebraic functions and function fields in algebraic geometry Large automorphism groups of ordinary curves of even genus in odd 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 \(x^n+y^m+1=0\) unlikely intersection; additive structure; multiplicative group Heights, Varieties over global fields, Rational points, Diophantine equations in many variables, Curves of arbitrary genus or genus \(\ne 1\) over global fields Unlikely intersections between additive and multiplicative structures
| 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 \(x^n+y^m+1=0\) descent on curves; curves over a perfect field Samir Siksek, Descent on Picard groups using functions on curves, Bull. Austral. Math. Soc. 66 (2002), no. 1, 119 -- 124. Arithmetic ground fields for curves, Picard groups, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry Descent on Picard groups using functions on 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 \(x^n+y^m+1=0\) Convex hull; hyperbolic geometry; Kleinian group; Teichmüller space Curves of arbitrary genus or genus \(\ne 1\) over global fields, Families, moduli of curves (analytic), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Transcendental methods of algebraic geometry (complex-analytic aspects) Modulus inequality for grafting and its application
| 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 \(x^n+y^m+1=0\) Euclidean geometry; spherical geometry; conics; projective geometry; special relativity Jennings, G.: Modern Geometry with Applications. Springer, New York (1994) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry, Elementary problems in Euclidean geometries, Elementary problems in hyperbolic and elliptic geometries, Classical or axiomatic geometry and physics, Algebraic functions and function fields in algebraic geometry, Special relativity, Projective analytic geometry Modern geometry with 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 \(x^n+y^m+1=0\) finite field; Jacobian; algebraic function field; class number; tower Algebraic functions and function fields in algebraic geometry, Finite fields (field-theoretic aspects) Effective bounds on class number and estimation for any step of towers of algebraic 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 \(x^n+y^m+1=0\) global function fields; Kummer criterion; divisibility; p-class groups Goss, D, Units and class groups in the arithmetic of function fields, Bull. Am. Math. Soc., 13, 131-132, (1985) Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry Units and class-groups in the arithmetic theory 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 \(x^n+y^m+1=0\) algebraic function fields; arithmetic subgroups; Bruhat-Tits trees; quotient graphs; special unitary groups Groups acting on trees, Other matrix groups over rings, Algebraic functions and function fields in algebraic geometry, Cohomology of groups, Linear algebraic groups over global fields and their integers, Cohomology of arithmetic groups Quotients of the Bruhat-Tits tree by arithmetic subgroups of special unitary groups
| 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 \(x^n+y^m+1=0\) Zhang, S: Geometry of algebraic points. In: Yang, L., Yau, S.T. (eds.) First International Congress of Chinese Mathematicians, Beijing, 1998. AMS/IP Stud. Adv. Math., vol. 20, pp. 185-198. American Mathematical Society/International Press, Providence, RI (2001) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves over global fields, Varieties over global fields, Heights, Rational points Geometry of algebraic 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 \(x^n+y^m+1=0\) heights; Siegel's Lemma; lattices Fukshansky, L, Algebraic points of small height missing union of varieties, J. Number Theory, 130, 2099-2118, (2010) Heights, Lattices and convex bodies (number-theoretic aspects), Algebraic numbers; rings of algebraic integers, Arithmetic theory of algebraic function fields, Arithmetic ground fields for curves Algebraic points of small height missing a union of varieties
| 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; plane algebraic curve Tutaj, H.: Geometric proof of M. Noether's genus formula, Universitatis iagellonicae acta Mathematica 30 (1993) Special algebraic curves and curves of low genus, Singularities of curves, local rings, Curves of arbitrary genus or genus \(\ne 1\) over global fields Geometric proof of M. Noether's genus formula
| 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; genus; morphism; Faltings theorem; Mordell conjecture; algebraic curve of genus greater than one; method of Demyanenko-Manin; rational points; height; Birch and Swinnerton-Dyer conjecture Kulesz, L.; Application de la méthode de Dem'janenko-Manin à certaines familles de courbes de genre 2 et 3; J. Number Theory: 1999; Volume 76 ,130-146. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves over global fields, Arithmetic ground fields for curves, Elliptic curves Application of the method of Dem'yanenko-Manin to certain families of curves of genus 2 or 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 \(x^n+y^m+1=0\) quadratic Chabauty; bielliptic curves; \(p\)-adic heights Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Arithmetic varieties and schemes; Arakelov theory; heights, Elliptic curves over global fields, Heights Explicit quadratic Chabauty over 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 \(x^n+y^m+1=0\) Nevanlinna theory; Picard-Berkovich's Theorem Boutabaa, A.; Escassut, A.: Parametrization of curves in characteristic p, Commentarii mathematici universitatis sancti Pauli 53, No. 2, 205-217 (2004) Algebraic functions and function fields in algebraic geometry, Non-Archimedean function theory Parametrization of curves 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 \(x^n+y^m+1=0\) tower of function fields; number of rational places; ihara's constant; cartier operator; \(p\)-rank N. Anbar, P. Beelen, N. Nguyen, A new tower meeting Zink's bound with good \(p\)-rank, appeared online 18 January 2017 in Acta Arithmetica. Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields, Applications to coding theory and cryptography of arithmetic geometry A new tower with good \(p\)-rank meeting Zink's bound
| 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 points; modular curves; bielliptic and hyperelliptic curves Bars, F.: Bielliptic modular curves. J. Number Theory 76 (1999), no. 1, 154-165. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Arithmetic ground fields for curves, Algebraic theory of abelian varieties Bielliptic modular 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 \(x^n+y^m+1=0\) Hurwitz bound; \(p\)-ranks; abelian subgroups of \(\Aut(X)\) Nakajima, S.: On automorphism groups of algebraic curves. In: Current Trends in Number Theory, pp. 129--134. Hindustan Book Agency, New Delhi (2002) Automorphisms of curves, Algebraic functions and function fields in algebraic geometry, Coverings of curves, fundamental group, Jacobians, Prym varieties On automorphism groups of algebraic 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 \(x^n+y^m+1=0\) Arakelov geometry; isoperimetric inequality; Brunn-Minkowski inequality Arithmetic varieties and schemes; Arakelov theory; heights, Curves of arbitrary genus or genus \(\ne 1\) over global fields On isoperimetric inequality in Arakelov geometry
| 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 \(x^n+y^m+1=0\) Shimura curves; special points; correspondences; dynamics Modular and Shimura varieties, Graphs and abstract algebra (groups, rings, fields, etc.), Infinite graphs, Algebraic functions and function fields in algebraic geometry, Arithmetic dynamics on general algebraic varieties Correspondences without a core
| 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 \(x^n+y^m+1=0\) equidistribution; group scheme; elliptic curve; abelian variety Elliptic curves over global fields, Arithmetic ground fields for abelian varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Well-distributed sequences and other variations Wieferich past and future
| 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 \(x^n+y^m+1=0\) \(R\)-equivalences; algebraic tori; pseudoglobal fields; Tate-Shafarevich groups; algebraic function fields Linear algebraic groups over global fields and their integers, Other nonalgebraically closed ground fields in algebraic geometry, Galois cohomology of linear algebraic groups, Arithmetic theory of algebraic function fields On the \(R\)-equivalence on algebraic tori over pseudoglobal 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 \(x^n+y^m+1=0\) Chabauty, Claude, Sur LES points rationnels des courbes algébriques de genre supérieur à l'unité, C. R. Acad. Sci. Paris, 212, 882-885, (1941), (French), MR0004484 Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus Sur les points rationnels des courbes algébriques de genre supérieur à l'unité
| 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 \(x^n+y^m+1=0\) Draziotis, K; Poulakis, D, Explicit Chevalley-Weil theorem for affine plane curves, Rocky Mt. J. Math., 39, 49-70, (2009) Plane and space curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Coverings of curves, fundamental group, Classification of affine varieties Explicit Chevalley-Weil theorem for affine plane 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 \(x^n+y^m+1=0\) hyperelliptic curves; integral points; curve of genus 2; rational points; effective bounds; Jacobian; theta divisor Grant, D.: Integer points on curves of genus two and their Jacobians. Trans. amer. Math. soc. 344, No. 1, 79-100 (1994) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Special algebraic curves and curves of low genus, Abelian varieties of dimension \(> 1\) Integer points on curves of genus 2 and their Jacobians
| 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 \(x^n+y^m+1=0\) zeta; multizeta; Bernoulli; Jacobians; zero distribution Dinesh S. Thakur , Power sums of polynomials over finite fields and applications: a survey , Finite Fields Appl. 32 (2015), p. 171-191 - ISSN : 2118-8572 (online) 1246-7405 (print) - Société Arithmétique de Bordeaux Arithmetic theory of polynomial rings over finite fields, Research exposition (monographs, survey articles) pertaining to number theory, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Multiple Dirichlet series and zeta functions and multizeta values, Zeta and \(L\)-functions in characteristic \(p\), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Jacobians, Prym varieties Power sums of polynomials over finite fields and applications: a survey
| 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 \(x^n+y^m+1=0\) Cohen-Macaulay property; associated graded ring S. Molinelli, D.P. Patil and G. Tamone, On the Cohen-Macaulayness of the associated graded ring of certain monomial curves , Beiträge zur Algebra und Geometrie \emdash/ Contributions to Algebra and Geometry 39 (1998), 433-446. Cohen-Macaulay modules, Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, Algebraic functions and function fields in algebraic geometry On the Cohen-Macaulayness of the associated graded ring of certain monomial 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 \(x^n+y^m+1=0\) Algebraic function fields Algebraic functions and function fields in algebraic geometry Algebraic investigations of the Riemann Roch Theorem.
| 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 \(x^n+y^m+1=0\) tensor products of cyclic algebras; division algebras of prime index; division algebras over function fields; cubic divisors; central division algebras; ramification divisors; Brauer groups; exponents Michel Van den Bergh, Division algebras on \?² of odd index, ramified along a smooth elliptic curve are cyclic, Algèbre non commutative, groupes quantiques et invariants (Reims, 1995) Sémin. Congr., vol. 2, Soc. Math. France, Paris, 1997, pp. 43 -- 53 (English, with English and French summaries). Finite-dimensional division rings, Arithmetic theory of algebraic function fields, Quaternion and other division algebras: arithmetic, zeta functions, Brauer groups of schemes Division algebras on \(\mathbb{P}^2\) of odd index, ramified along a smooth elliptic curve are cyclic
| 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; exponential function; Drinfeld module; lattice; analog of Siegel's lemma; Hilbert's 7th problem Yu, J.: Transcendence theory over function fields. Duke math. J. 52, 517-527 (1985) Transcendence theory of Drinfel'd and \(t\)-modules, Drinfel'd modules; higher-dimensional motives, etc., Algebraic functions and function fields in algebraic geometry Transcendence theory 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 \(x^n+y^m+1=0\) factorial domain; half-factorial domain; Fermat curves Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial), Divisibility and factorizations in commutative rings, Algebraic functions and function fields in algebraic geometry Factorial Fermat curves over the rational numbers
| 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 and function fields in algebraic geometry, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) Newton diagrams and algebraic 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 group of fields of rational functions on algebraic varieties over number fields; Bloch-Kato conjecture F.\ A. Bogomolov, On two conjectures in birational algebraic geometry, Algebraic geometry and analytic geometry (Tokyo 1990), ICM-90 Satell. Conf. Proc., Springer, Tokyo (1991), 26-52. Algebraic functions and function fields in algebraic geometry, (Co)homology theory in algebraic geometry, Galois cohomology, Rational and birational maps, Varieties over global fields On two conjectures in birational algebraic geometry
| 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 \(x^n+y^m+1=0\) superelliptic curve; Jacobian variety; twist theory Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Plane and space curves A certain quadruple family of superelliptic curves associated with \((p,p)\)-extension
| 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 forms; birational equivalence Quadratic forms over general fields, Algebraic theory of quadratic forms; Witt groups and rings, Quadratic spaces; Clifford algebras, Forms and linear algebraic groups, Clifford algebras, spinors, Transcendental field extensions, Algebraic functions and function fields in algebraic geometry Some criteria for stably birational equivalence of quadratic forms
| 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; genus; Cartier operator Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry A note on algebraic curves 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 \(x^n+y^m+1=0\) birational classification of real rational surfaces; classification of function fields; ruled surface Silhol, R., Classification birationnelle des surfaces rationnelles réelles, 308-324, (1990), Berlin Special surfaces, Topology of real algebraic varieties, Rational and birational maps, Families, moduli, classification: algebraic theory, Arithmetic theory of algebraic function fields Birational classification of real rational surfaces
| 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; curves over finite fields; cyclic covers Curves over finite and local fields, Other abelian and metabelian extensions, Arithmetic theory of algebraic function fields, Rational points On the distribution of the rational points on cyclic covers in the absence of roots of unity
| 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; Kummer extensions; Weierstrass semigroups; Weierstrass pure gap Hu, C.; Yang, S., Multi-point codes over Kummer extensions, Des. Codes Cryptogr., 86, 211-230, (2018) Riemann surfaces; Weierstrass points; gap sequences, Arithmetic theory of algebraic function fields Multi-point codes over Kummer 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 \(x^n+y^m+1=0\) abelian varieties; superelliptic jacobians; doubly transitive permutation groups. Yu. G. Zarhin, ''Endomorphisms of Superelliptic Jacobians,'' Math. Z. 261, 691--707, 709 (2009). Jacobians, Prym varieties, Algebraic theory of abelian varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\) Endomorphisms of superelliptic Jacobians
| 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 geometry; Lang's conjecture; fibered power conjecture; uniformity of rational points; varieties of general type; positive characteristic Dan Abramovich and José Felipe Voloch, Lang's conjectures, fibered powers, and uniformity, New York J. Math. 2 (1996), 20 -- 34, electronic. Arithmetic varieties and schemes; Arakelov theory; heights, Rational points, Algebraic functions and function fields in algebraic geometry Lang's Conjectures, Fibered Powers, and Uniformity
| 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; integral points; Siegel's theorem Alvanos, P.; Bilu, Y.; Poulakis, D., \textit{characterizing algebraic curves with infinitely many integral points}, Int. J. Number Theory, 5, 585-590, (2009) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Counting solutions of Diophantine equations Characterizing algebraic curves with infinitely many integral 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 \(x^n+y^m+1=0\) rational points; algebraic curves; \(C\)-function Rational points, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Curves of arbitrary genus or genus \(\ne 1\) over global fields Arithmetic on 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 \(x^n+y^m+1=0\) abelian variety; polynomial Pell equation; abelian scheme; flat subgroup scheme; elliptic surface Algebraic theory of abelian varieties, Elliptic curves over global fields, Global ground fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Heights, Model theory (number-theoretic aspects) Unlikely intersections in families of abelian varieties and the polynomial Pell equation
| 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 \(x^n+y^m+1=0\) Heß, F.: An algorithm for constructing Weierstrass points, Lecture notes in comput. Sci. 2369, 357-371 (2002) Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences An algorithm for computing Weierstrass 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 \(x^n+y^m+1=0\) algebraic functions Bliss, G. A. (1933). \textit{Algebraic functions} (Vol. XVI). Providence, RI: American Mathematical Society Colloquium Publications. Research exposition (monographs, survey articles) pertaining to algebraic geometry, Algebraic functions and function fields in algebraic geometry 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 \(x^n+y^m+1=0\) algebraic calculus; equation of cylindroids; descriptive properties of curves; projective properties of curves; hyperbolic sine; hyperbolic cosine; Hamilton`s biquarternions Algebraic functions and function fields in algebraic geometry, Plane and space curves, Exponential and trigonometric functions, Classical hypergeometric functions, \({}_2F_1\), Hyperbolic and elliptic geometries (general) and generalizations On the application of quaternions and Grassmann's Ausdehnungslehre to different kinds of uniform space.
| 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 \(x^n+y^m+1=0\) Polynomials over finite fields; Curves over finite fields with many rational points Deolalikar, V., Extensions of algebraic function fields with complete splitting of all rational places, Comm. Algebra, 30, 6, 2687-2698, (2002) Curves over finite and local fields, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields Extensions of algebraic function fields with complete splitting of all 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 \(x^n+y^m+1=0\) integrability of Birkhoff billiards; algebraic curves S. V. Bolotin, ''Integrable billiards of Birkhoff,'' \textit{Vestn. Mosk. Univ. Ser. 1 Mat. Mekh.}, No. 2, 33-36 (1990). Ergodic theory, Algebraic functions and function fields in algebraic geometry Integrable Birkhoff billiards
| 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 pairs; dessins d'enfants; action of the absolute Galois group; monodromy group; cartographic group; plane trees Jones, G.A., Streit, M.: Galois groups, monodromy groups and cartographic groups. In: Schneps L., Lochak P. (eds) Geometric Galois Actions, 2. LMS Lecture Notes Series 243. Cambridge University Press, Cambridge, (1997) Arithmetic ground fields for curves, Group actions on varieties or schemes (quotients), Global ground fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Galois theory Galois groups, monodromy groups and cartographic groups
| 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 \(x^n+y^m+1=0\) Resolution of curve singularities. Class numbers of curves Algebraic functions and function fields in algebraic geometry, Singularities of curves, local rings On the system of singular values of an algebraic function and the singular points 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 \(x^n+y^m+1=0\) rational points; curves; solvability; local-to-global obstruction; descent N. Bruin, M. Stoll, Deciding existence of rational points on curves: an experiment, Experiment. Math. 17 (2008), 181-189. Zbl1218.11065 MR2433884 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Higher degree equations; Fermat's equation, Computer solution of Diophantine equations, Rational points, Computational aspects of algebraic curves Deciding existence of rational points on curves: an experiment
| 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 \(x^n+y^m+1=0\) smooth hypersurfaces; \(K3\) surfaces; Galois point; quartic surface Takahashi T.: Galois points on normal quartic surfaces. Osaka J. Math. 39, 647--663 (2002) Hypersurfaces and algebraic geometry, Separable extensions, Galois theory, \(K3\) surfaces and Enriques surfaces, Algebraic functions and function fields in algebraic geometry, Singularities of surfaces or higher-dimensional varieties Galois points on normal quartic surfaces.
| 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 \(x^n+y^m+1=0\) monodromy group; symmetric and alternating group Robert M. Guralnick and John Shareshian. Symmetric and alternating groups as monodromy groups of Riemann surfaces. I. Generic covers and covers with many branch points. Mem. Amer. Math. Soc., 189(886):vi+128, 2007. With an appendix by Guralnick and R. Stafford. Coverings of curves, fundamental group, Primitive groups, Algebraic functions and function fields in algebraic geometry Symmetric and alternating groups as monodromy groups of Riemann surfaces. I: Generic covers and covers with many branch points. With an appendix by R. Guralnick and R. Stafford
| 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 \(x^n+y^m+1=0\) Frobenius group; monodromy group; coverings of curves; algebraic function field Coverings of curves, fundamental group, Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory, Finite automorphism groups of algebraic, geometric, or combinatorial structures Frobenius groups as monodromy groups
| 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 surface family of \(2^nd\) degree; orthogonal system; algebraic; concentric; rectangular; equation; parameter; O.D.E.; elimination resultant; Darboux; class of curves; cyclic; confocal Families, moduli, classification: algebraic theory, Quadratic and bilinear forms, inner products, Polar geometry, symplectic spaces, orthogonal spaces, Surfaces in Euclidean and related spaces, Equations in general fields, Implicit ordinary differential equations, differential-algebraic equations, Algebraic functions and function fields in algebraic geometry About the most general family of \(2^nd\) degree surfaces, that forms an orthogonal system with any two other surface families.
| 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 on curves; Chabauty's method; Selmer group Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Global ground fields in algebraic geometry, Arithmetic ground fields for curves, Computer solution of Diophantine equations, Higher degree equations; Fermat's equation Chabauty without the Mordell-Weil 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 \(x^n+y^m+1=0\) Prasad, D.; Rajan, C. S., On an Archimedean analogue of tate's conjecture, J. Number Theory, 99, 180-184, (2003) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Isospectrality, Riemann surfaces; Weierstrass points; gap sequences On an Archimedean analogue of Tate'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 \(x^n+y^m+1=0\) Schottky-Klein formulae; hyperelliptic sigma functions; Jacobian V. Enolskii, S. Matsutani, and Y. Ônishi, ''The Addition Law Attached to a Stratification of a Hyperelliptic Jacobian Variety,'' Tokyo J. Math. 31(1), 27--38 (2008); arXiv:math.AG/0508366. Algebraic functions and function fields in algebraic geometry, Subvarieties of abelian varieties, Special algebraic curves and curves of low genus, Special divisors on curves (gonality, Brill-Noether theory) The addition law attached to a stratification of a hyperelliptic Jacobian variety
| 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 \(x^n+y^m+1=0\) Kowalewski's curve; Bobenko-Reyman-Semenov-Tian-Shansky curve; curves of genus 2; Kowalewski top; Jacobians; theta-functions; isogeny; Richelot's transformation; Hamiltonian flows; Prym varieties Markushevich, D., Kowalevski Top and Genus-2 Curves, J. Phys. A: Math. Gen., 2001, vol. 34, pp. 2125--2135. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions Kowalevski top and genus-2 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 \(x^n+y^m+1=0\) automorphism groups; rational points; maximal curves; function fields Bassa, A.; Ma, L.; Xing, C.; Yeo, S. L., Toward a characterization of subfields of the Deligne-Lusztig function fields, \textit{J. Comb. Theory Ser. A}, 120, 1351-1371, (2013) Combinatorial aspects of representation theory, Curves over finite and local fields, Finite ground fields in algebraic geometry, Automorphisms of curves, Arithmetic theory of algebraic function fields Towards a characterization of subfields of the Deligne-Lusztig 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; bounds for the height of rational points; torsion; canonical height; integral points; elliptic curves Elliptic curves over global fields, Arithmetic theory of algebraic function fields, Heights, Rational points Integral points on elliptic curves over function 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 \(x^n+y^m+1=0\) indecomposable modules; divisible modules; injective modules; Jacobians; dual of Heller's loop operator Rzedowski-Calderón M., Mejía-Huguet V.J.: Indescomponibilidad y módulos -divisibles. Aport. Mat. Comun. 35, 45--63 (2005) Injective and flat modules and ideals in commutative rings, Jacobians, Prym varieties, Arithmetic theory of algebraic function fields, Injective modules, self-injective associative rings, Group rings of finite groups and their modules (group-theoretic aspects) Indecomposability and \(\ell\)-divisible 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 \(x^n+y^m+1=0\) rational base points; linear pencil of plane curves Pencils, nets, webs in algebraic geometry, Plane and space curves, Families, moduli of curves (algebraic), Rational points, Algebraic functions and function fields in algebraic geometry On \(\mathbb{Q}\)-split Bézout intersection
| 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 \(x^n+y^m+1=0\) metrized graph; polarized metrized graph; invariants of polarized metrized graphs; tau constant; resistance function; discrete Laplacian matrix; pseudo inverse; relative dualizing sheaf Cinkir, Z.: Computation of Polarized metrized graph invariants by using discrete laplacian matrix. Math. Comp. 10.1090/mcom/2981 Graphs and linear algebra (matrices, eigenvalues, etc.), Graph algorithms (graph-theoretic aspects), Distance in graphs, Arithmetic varieties and schemes; Arakelov theory; heights, Programming involving graphs or networks, Applications of graph theory to circuits and networks, Heights, Varieties over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields Computation of polarized metrized graph invariants by using discrete Laplacian matrix
| 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; Jacobian; Galois conjugates Global ground fields in algebraic geometry, Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields Algebraic points of degree at most 2 on the affine curve \(y^{11} = x^2 (x - 1)^2\)
| 0 |
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