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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 \(x^n+y^m+1=0\) Azumaya algebras; Brauer gropus; Brauer-Manin obstruction; Hasse principle; hyperelliptic curves Rational points, Varieties over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields From separable polynomials to nonexistence of rational points on certain hyperelliptic 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 \(x^n+y^m+1=0\) Prym varieties; Chabauty methods; rational points on curves; covering technique; Brauer-Manin; smooth plane quartics Bruin, N, The arithmetic of Prym varieties in genus 3, Compos. Math, 144, 317-338, (2008) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties The arithmetic of Prym varieties in genus 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 \(x^n+y^m+1=0\) bielliptic curves; hyperelliptic curves; classical modular curves; quadratic points Arithmetic aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Arithmetic ground fields for curves, Algebraic theory of abelian varieties, Research exposition (monographs, survey articles) pertaining to number theory On quadratic points of classical 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 \(x^n+y^m+1=0\) \(n\)-th Gauss map; intersection multiplicities; non-classical curves; order sequence; dual varieties Hefez A., Kakuta N.: On the geometry of non-classical curves. Bol. Soc. Bras. Mat. 23(1)(2), 79--91 (1992). Algebraic functions and function fields in algebraic geometry, Topological properties in algebraic geometry, Rational and birational maps On the geometry of non-classical 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 \(x^n+y^m+1=0\) number of mappings of algebraic curves; theorem of De Franchis; Mordell's conjecture over functions fields Algebraic functions and function fields in algebraic geometry, Rational and birational maps, Picard-type theorems and generalizations for several complex variables, Enumerative problems (combinatorial problems) in algebraic geometry, Global ground fields in algebraic geometry A higher dimensional analogue of Mordell's conjecture over function fields and related problems | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Abhyankar valuations; multiplier ideals Li, C.: Yau-Tian-Donaldson correspondence for K-semistable Fano varieties. Journal für die reine und angewandte Mathematik (Crelles journal). arXiv:1302.6681 (\textbf{to appear}) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Ideals and multiplicative ideal theory in commutative rings, Algebraic functions and function fields in algebraic geometry Uniform approximation of Abhyankar valuation ideals in smooth 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 \(x^n+y^m+1=0\) Hyperelliptic curves; Montgomery arithmetic; fast arithmetic; cryptographic applications T. Lange. Montgomery Addition for Genus Two Curves. In Algorithmic Number Theory Seminar ANTS-VI, volume 3076 of Lect. Notes Comput. Sci., pages 309-317, 2004. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Applications to coding theory and cryptography of arithmetic geometry, Cryptography Montgomery addition for genus two 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 substitutions Morphisms of commutative rings, Algebraic functions and function fields in algebraic geometry, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Linear transformations, semilinear transformations, Multilinear and polynomial operators Treatise on algebraic substitutions. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) transcendental invariant subfield; rational function field; automorphisms Chu, H, Orthogonal group actions on rational function fields, Bull. Inst. Math. Acad. Sinica, 16, 115-122, (1988) Geometric invariant theory, Arithmetic theory of algebraic function fields, Transcendental field extensions, Group actions on varieties or schemes (quotients) Orthogonal 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 \(x^n+y^m+1=0\) rational triangle; congruent number; envelope; \(\theta\)-congruent number Elliptic curves over global fields, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Quadratic and bilinear Diophantine equations New generalizations of congruent 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 \(x^n+y^m+1=0\) N. Bruin, M. Stoll,The Mordell-Weil sieve: Proving non-existence of rational points on curves, LMS J. Comput. Math. 13 (2010), 272-306. MR2685127 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computer solution of Diophantine equations, Rational points The Mordell-Weil sieve: proving non-existence of 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 \(x^n+y^m+1=0\) curves defined over fields of formal power series; reciprocity law; bad reduction Douai, Jean-Claude; Touibi, Chedly: Courbes définies sur LES corps de séries formelles et loi de réciprocité. Acta arith. 42, No. 1, 101-106 (1982/1983) Arithmetic theory of algebraic function fields, Galois cohomology, Galois cohomology, Coverings in algebraic geometry, Étale and other Grothendieck topologies and (co)homologies, Global ground fields in algebraic geometry, Arithmetic ground fields for curves Curves defined over fields of formal power series, and a reciprocity law | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebro-geometric codes Linear codes (general theory), Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry Codes and 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 \(x^n+y^m+1=0\) proper projection; plurisubharmonic function; BMO-function; algebraic variety; Bernstein inequality; algebraic functions A. Brudnyi (1997): A Bernstein-type inequality for algebraic functions. Indiana Univ. Math. J., 46:93--116. Real polynomials: analytic properties, etc., Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities), \(H^p\)-spaces, Algebraic functions and function fields in algebraic geometry, Plurisubharmonic functions and generalizations A Bernstein-type inequality for algebraic functions | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) elliptic curves over function fields; bad reduction; \(j\)-invariant; function field; Weierstrass equation Arithmetic theory of algebraic function fields, Elliptic curves, Elliptic curves over global fields, Elliptic curves over local fields Minimal number of points with bad reduction for elliptic curves over \(\mathbb{P}^1\) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 function field; hyperelliptic curve; divisor class group Sachar Paulus and Andreas Stein, Comparing real and imaginary arithmetics for divisor class groups of hyperelliptic curves, Algorithmic number theory (Portland, OR, 1998) Lecture Notes in Comput. Sci., vol. 1423, Springer, Berlin, 1998, pp. 576 -- 591. Algebraic number theory computations, Computational aspects of algebraic curves, Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Applications to coding theory and cryptography of arithmetic geometry Comparing real and imaginary arithmetics for divisor class groups of hyperelliptic 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 \(x^n+y^m+1=0\) modular group; combinatorial group theory; free group; unity; generating function; algebraic function; cogrowth rate; return generating function; word problem; pushdown automaton Permutations, words, matrices, Exact enumeration problems, generating functions, Generators, relations, and presentations of groups, Algebraic functions and function fields in algebraic geometry The modular group and words in its two generators | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) non-standard analysis; plane curves; standard points; infinitesimal; passage to the shadow Nonstandard analysis, Algebraic functions and function fields in algebraic geometry, Singularities of curves, local rings Calculating the metric invariants associated with 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 \(x^n+y^m+1=0\) curves; rational points; Chabauty; Coleman; Mordell-Weil sieve Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Arithmetic ground fields for curves Chabauty and the Mordell-Weil sieve | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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-Coleman method; rational points; hyperelliptic curves Algebraic number theory computations, Computational aspects of algebraic curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Curves over finite and local fields, Coverings of curves, fundamental group, Special algebraic curves and curves of low genus Chabauty-Coleman experiments for genus 3 hyperelliptic 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 \(x^n+y^m+1=0\) Javanpeykar, A, Néron models and the arithmetic Shafarevich conjecture for certain canonically polarized surfaces, Bull. Lond. Math. Soc., 47, 55-64, (2015) Arithmetic ground fields for curves, Families, moduli of curves (algebraic), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry Néron models and the arithmetic Shafarevich conjecture for certain canonically polarized 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 \(x^n+y^m+1=0\) Artin braid group; Jacobian varieties; Hurwitz monodromy; moduli space of curves M. Fried, Combinatorial computation of moduli dimension of Nielsen classes of covers, Contemporary Mathematics 89 (1989), 61--79. Coverings of curves, fundamental group, Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry, Algebraic moduli problems, moduli of vector bundles, Separable extensions, Galois theory, Families, moduli of curves (algebraic), Coverings in algebraic geometry Combinatorial computation of moduli dimension of Nielsen classes of 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 \(x^n+y^m+1=0\) Artin L-functions; smooth projective curve over a finite field; places; Euler characteristic; Galois cohomology Bae, S.: On the conjectures of Lichtenbaum and Chinburg over function fields. Math. Ann. 285, 417--445 (1989) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic ground fields for curves, Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Galois cohomology On the conjecture of Lichtenbaum and of Chinburg 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 \(x^n+y^m+1=0\) cyclotomic function field; Carlitz module; Riemann-Hurwitz formula Riemann surfaces; Weierstrass points; gap sequences, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Curves over finite and local fields, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Automorphisms of curves, Modules of differentials Explicit Galois representations of automorphisms on holomorphic differentials 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 \(x^n+y^m+1=0\) Fermat equations; generalized Fermat equations S. Siksek and M. Stoll, Partial descent on hyperelliptic curves and the generalized Fermat equation \(x\)\^{}\{3\} + \(y\)\^{}\{4\} + \(z\)\^{}\{5\} = 0, Bull. London Math. Soc. \textbf{44} (2012), 151-166. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Varieties over global fields, Analytic theory of abelian varieties; abelian integrals and differentials, Divisors, linear systems, invertible sheaves Partial descent on hyperelliptic curves and the generalized Fermat equation \(x^3+y^4+z^5=0\) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; periods; Jacobian Nullwerte Jordi Guàrdia, Jacobian Nullwerte, periods and symmetric equations for hyperelliptic curves, Ann. Inst. Fourier (Grenoble) 57 (2007), no. 4, 1253 -- 1283 (English, with English and French summaries). Curves of arbitrary genus or genus \(\ne 1\) over global fields, Theta functions and abelian varieties Jacobian Nullwerte, periods and symmetric equations for hyperelliptic 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 \(x^n+y^m+1=0\) Jacobian; function field; Abel-Jacobi embedding; Bogomolov's conjecture A. Moriwaki, Bogomolov conjecture for curves of genus 2 over function fields, J. Math. Kyoto Univ. 36 (1996), 687-695. Algebraic functions and function fields in algebraic geometry, Jacobians, Prym varieties, Arithmetic ground fields for curves Bogomolov conjecture for curves of genus 2 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 functions of one variable Algebraic functions and function fields in algebraic geometry 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 \(x^n+y^m+1=0\) rigid-analytic period functions; Goss polynomials; distribution of zeros of \(p\)-adic functions Arithmetic theory of algebraic function fields, Modular forms associated to Drinfel'd modules, Rigid analytic geometry On the zeroes of certain periodic functions over valued 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 \(x^n+y^m+1=0\) classification up to isomorphism; elementary equivalence; function fields over algebraically closed fields; function fields of curves; elliptic curves D. Pierce , Function fields and elementary equivalence . Bull. London Math. Soc. 31 ( 1999 ), 431 - 440 . MR 1687564 | Zbl 0959.03022 Model-theoretic algebra, Algebraic functions and function fields in algebraic geometry, Elliptic curves, Model theory (number-theoretic aspects), Properties of classes of models Function fields and elementary equivalence | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 code; asymptotic bounds; Tsfasman-Vladut-Zink bound Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Bounds on codes, Arithmetic theory of algebraic function fields Improved algebraic geometry bounds | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; genus; geometry of numbers D. Kettlestrings and J.L. Thunder, The number of function fields with given genus, Contem. Math. 587 (2013), 141--149. Arithmetic theory of algebraic function fields, Global ground fields in algebraic geometry The number of function fields with given genus | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Compact Riemann surfaces and uniformization, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Fuchsian groups and their generalizations (group-theoretic aspects), Theta series; Weil representation; theta correspondences, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Algebraic functions and function fields in algebraic geometry, Kleinian groups (aspects of compact Riemann surfaces and uniformization) Uniformizations of Riemann surfaces: Poincaré theta series, Riemann's theta function and theta 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 \(x^n+y^m+1=0\) Weierstrass semigroup; Kummer extension; Weierstrass gap Yang, S.; Hu, C., Weierstrass semigroups from Kummer extensions, Finite Fields Appl., 45, 264-284, (2017) Riemann surfaces; Weierstrass points; gap sequences, Arithmetic theory of algebraic function fields Weierstrass semigroups from 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 \(x^n+y^m+1=0\) constant composition codes; difference families; difference systems of sets; perfect nonlinear functions; permutation functions; zero-difference balanced functions Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.), Combinatorial aspects of block designs, Factorials, binomial coefficients, combinatorial functions, Algebraic functions and function fields in algebraic geometry, Other types of codes Zero-difference balanced functions 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 \(x^n+y^m+1=0\) harmonic maps; finiteness problems; topological map homotopic to a holomorphic map; fibration by holomorphic curves; period map; compactified moduli variety; Arakelov theorem; Mordell conjecture; Kähler manifolds; variations of the singular set of families over a curve Jürgen Jost and Shing-Tung Yau, Harmonic mappings and algebraic varieties over function fields, Amer. J. Math. 115 (1993), no. 6, 1197 -- 1227. Families, fibrations in algebraic geometry, Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables, Global differential geometry of Hermitian and Kählerian manifolds, Algebraic functions and function fields in algebraic geometry, Singularities of curves, local rings Harmonic mappings and algebraic varieties over function fields | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field of a smooth projective curve; characteristic \(p\); \(abc\) theorem [Sc] T. Scanlon: ''The abc theorem for commutative algebraic groups in characteristic p'', Int. Math. Res. Notices, No. 18, (1997), pp. 881--898. Arithmetic ground fields for abelian varieties, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry The \(abc\) theorem for commutative algebraic groups 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 \(x^n+y^m+1=0\) function fields; transcendental extensions; Lüroth theorem; orderable subfield Recio, T., Sendra, J.R.: A really elementary proof of real Lüroth's theorem. Rev. Mat. Univ. Complut. Madrid, \textbf{10}(Special Issue, suppl.), 283-290 (1997) Transcendental field extensions, Real and complex fields, Algebraic functions and function fields in algebraic geometry, Real algebraic sets A really elementary proof of real Lüroth's 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 \(x^n+y^m+1=0\) arithmetic groups; global function field; Drinfeld symmetric space; compactification; modular forms; Stark's conjectures Gekeler, E.-U., Satake compactification of Drinfel'd modular schemes, (de Grande-de Kimpe, N.; van Hamme, L., Proceedings of the conference on \textit{p}-adic analysis, Houthalen, 1986, (1987), Vrije Univ. Brussel Brussels), 71-81 Global ground fields in algebraic geometry, Structure of modular groups and generalizations; arithmetic groups, Arithmetic theory of algebraic function fields, Theta series; Weil representation; theta correspondences, Formal groups, \(p\)-divisible groups, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Satake compactification of Drinfeld modular schemes | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Francisco Javier Cirre, Birational classification of hyperelliptic real algebraic curves, The geometry of Riemann surfaces and abelian varieties, Contemp. Math., vol. 397, Amer. Math. Soc., Providence, RI, 2006, pp. 15 -- 25. Real algebraic sets, Klein surfaces, Algebraic functions and function fields in algebraic geometry, Rational and birational maps Birational classification of hyperelliptic real 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 \(x^n+y^m+1=0\) linear algebraic group; torsor; function field; local-global principle; Galois cohomology David Harbater, Julia Hartmann, and Daniel Krashen. Local-global principles for torsors over arithmetic curves. Amer.\ J.\ Math., \textbf{137}(6) (2015), 1559--1612. DOI 10.1353/ajm.2015.0039; zbl 1348.11036; MR3432268; arxiv 1108.3323 Galois cohomology of linear algebraic groups, Algebraic functions and function fields in algebraic geometry, Rational points, Algebraic theory of quadratic forms; Witt groups and rings Local-global principles for torsors over arithmetic 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 sum of a bundle on a singular curve Algebraic functions and function fields in algebraic geometry On the Abel-Jacobi theorem for singular 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 \(x^n+y^m+1=0\) Jacobi theta function; holomorphic maps of curves; Laurent coefficients; quasi-modular forms; Jacobi forms M. Kaneko and D. Zagier, A generalized Jacobi theta function and quasimodular forms, in \textit{The moduli space of curves (Texel Island, 1994)}, 165--172, Progr. Math., 129, Birkhäuser Boston, Boston, MA, 1995.Zbl 0892.11015 MR 1363056 Holomorphic modular forms of integral weight, Theta functions and abelian varieties, Theta functions and curves; Schottky problem, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Other groups and their modular and automorphic forms (several variables) A generalized Jacobi theta function and quasimodular 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 \(x^n+y^m+1=0\) isotropic plane; circular cubic curves; Tridens Euclidean geometries (general) and generalizations, Analytic geometry with other transformation groups, Algebraic functions and function fields in algebraic geometry Über zirkuläre Kurven 3. Ordnung der isotropen Ebene. (About circular cubic curves in isotropic planes) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 congruences; Laurent expansion; elliptic functions; nonsingular cubic curve; Hessian normal form; generalized Von Staudt-Clausen partial fraction decompositions C. Snyder, The coefficients of the Hessian elliptic functions, J. Reine Angew. Math. 306, 60--87. Arithmetic theory of algebraic function fields, Bernoulli and Euler numbers and polynomials, Special algebraic curves and curves of low genus, Elliptic curves Partial fraction decompositions and Kummer congruences for the normalized coefficients of the Laurent expansion of elliptic functions parametrizing a nonsingular cubic curve in Hessian normal 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 \(x^n+y^m+1=0\) algebraic function integration problem Computational aspects of algebraic curves, Symbolic computation and algebraic computation, Algebraic functions and function fields in algebraic geometry On the implementation of a new algorithm for the computation of hyperelliptic integrals | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) group representations; normal varieties; Galois stratification; Davenport pair; monodromy group; primitive group; covers; fiber products; open image theorem; Riemann's existence theorem; genus zero problem M. D. Fried, Variables separated equations: strikingly different roles for the branch cycle lemma and the finite simple group classification, Sci. China Math. 55(1) (2012), 1--72. Field arithmetic, Arithmetic aspects of modular and Shimura varieties, Arithmetic theory of algebraic function fields, Polynomials in general fields (irreducibility, etc.), Separable extensions, Galois theory, Coverings of curves, fundamental group, Finite simple groups and their classification Variables separated equations: strikingly different roles for the branch cycle lemma and the finite simple group classification | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 arithmetic; function fields Field arithmetic, Algebraic functions and function fields in algebraic geometry Embeddings of function fields into ample 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 discrete logarithm problem Itoh Toshiya, Sakurai Kouichi, Shizuya Hiruki. On the complexity of hyperelliptic discrete logarithm problem. InAdvances in EUROCRYPT'91, LNCS 547, Springer-Verlag, Brighton, UK, 1991, pp.337--351. Analysis of algorithms and problem complexity, Geometric methods (including applications of algebraic geometry) applied to coding theory, Algebraic coding theory; cryptography (number-theoretic aspects), Algebraic functions and function fields in algebraic geometry, Complexity classes (hierarchies, relations among complexity classes, etc.) On the complexity of hyperelliptic discrete logarithm problem | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 module generators; ring of algebraic integers; ray class field; maximal order; elliptic function M. J. Taylor: Relative Galois module structure of rings of integers and elliptic functions II. Ann. of Math., 121, 519-535 (1985). JSTOR: Galois theory, Elliptic functions and integrals, Integral representations related to algebraic numbers; Galois module structure of rings of integers, Algebraic functions and function fields in algebraic geometry, Quaternion and other division algebras: arithmetic, zeta functions Relative Galois module structure of rings of integers and elliptic functions. II | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Iwasawa theory of totally real number fields; covering of algebraic curves over a finite field; Drinfel'd modules; Picard group; L-series David Goss, The theory of totally real function fields, Applications of algebraic \?-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 449 -- 477. Coverings of curves, fundamental group, Totally real fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry The theory of totally real 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 \(x^n+y^m+1=0\) Weierstrass point; quartic; hyperflex; Jacobian Girard, M., The group of Weierstrass points of a plane quartic with at least eight hyperflexes, Math. Comp., 75, 1561-1583, (2006) Riemann surfaces; Weierstrass points; gap sequences, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computational aspects of algebraic curves, Jacobians, Prym varieties The group of Weierstrass points of a plane quartic with at least eight hyperflexes | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Clifford algebra of a binary form; relative Brauer group; conjugate splittings Haile, D.: On Clifford algebras, conjugate splittings, and function fields of curves. Israel math. Conf. proc. 1, 356-361 (1989) Brauer groups of schemes, Algebraic functions and function fields in algebraic geometry, Algebras and orders, and their zeta functions, General binary quadratic forms On Clifford algebras, conjugate splittings, and function fields of curves | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism group; Galois covering Compact Riemann surfaces and uniformization, Algebraic functions and function fields in algebraic geometry Über die Automorphismengruppen einer Klasse von kompakten Riemannschen Flächen. (On the automorphism group of a class of compact 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 \(x^n+y^m+1=0\) function field; prime divisor; Galois theory Pop, F, Pro-\(\mathcall \) abelian-by-central Galois theory of prime divisors, Isr. J. Math., 180, 43.68, (2010) Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry Pro-\(\ell\) abelian-by-central Galois theory of prime divisors | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; obstruction to the Hasse principle; Severi-Brauer varieties; quadrics; fields of rational functions Brauer groups of schemes, Global ground fields in algebraic geometry, Varieties over global fields, Arithmetic theory of algebraic function fields The Hasse principle for Brauer groups of function fields on the products of Severi-Brauer varieties and projective quadrics | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; 5-adic field; extended 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. III | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) generic division algebra; generic n\(\times n\) matrices; stable rationality; centre; moduli spaces; cellular decomposition conjecture; finite-dimensional hereditary algebras; zeta-functions; tori-invariants Division rings and semisimple Artin rings, Vector and tensor algebra, theory of invariants, Rings with polynomial identity, Endomorphism rings; matrix rings, Arithmetic theory of algebraic function fields, Families, moduli of curves (algebraic) Centers of generic division algebras | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) torsion points; Fermat Jacobians; curves of genus 1; rational points; Fermat curve Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Rational points Torsion points on Fermat 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 \(x^n+y^m+1=0\) I. OYAMA: On uniform convergence of trigonometrical series, (in the press) Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences Zur Theorie der hyperabelschen Funktionen. I, II, III, IV | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; Jacobians; sextactic points; Kuribayashi quartic curves Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus, Jacobians, Prym varieties Group generated by total sextactic points of Kuribayashi quartic 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 \(x^n+y^m+1=0\) Principle of assignment; algebraic forms; relation of conjugation; binary forms; theorems; odd degree; power of linear factors; curves of \(n^th\) order; connection lines; researches Axiomatics of classical set theory and its fragments, Forms over real fields, Algebraic functions and function fields in algebraic geometry, Relational systems, laws of composition, General binary quadratic forms, Forms of degree higher than two, Classical propositional logic, Power series rings, Plane and space curves, \(n\)-dimensional polytopes About a principle of attributing algebraic 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 \(x^n+y^m+1=0\) infrastructure; fractional ideal; purely cubic function field Renate Scheidler, Ideal arithmetic and infrastructure in purely cubic function fields, J. Théor. Nombres Bordeaux 13 (2001), no. 2, 609 -- 631 (English, with English and French summaries). Arithmetic theory of algebraic function fields, Elliptic curves, Computational aspects and applications of commutative rings Ideal arithmetic and infrastructure in purely cubic 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 extensions; inverse Galois theory; specialization; parametric extensions; twisting Dèbes, Pierre, Groups with no parametric Galois realizations, Ann. sci. éc. norm. supér., (2016), in press Inverse Galois theory, Arithmetic theory of algebraic function fields, Coverings in algebraic geometry, Ramification problems in algebraic geometry, Field arithmetic Groups with no parametric Galois realizations | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves; algebraic function fields; positive characteristic; automorphism groups Automorphisms of curves, Algebraic functions and function fields in algebraic geometry Curves with more than one inner Galois point | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 surfaces; elliptic curves; Nagao's conjecture; Mordell-Weil rank Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves Rational points on quadratic elliptic 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 \(x^n+y^m+1=0\) algebraic curves; algebraic function fields; positive characteristic; automorphism groups Automorphisms of curves, Algebraic functions and function fields in algebraic geometry Large odd prime power order automorphism groups of algebraic curves in any 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 \(x^n+y^m+1=0\) canonical height; logarithmic discriminant; height equality; logarithmic canonical class inequality; Bogomolov-Miyaoka-Yau inequality Tan S.-L, J. Reine Angew. Math. 461 pp 123-- (1995) Algebraic functions and function fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Rational points Height inequality of algebraic points on curves over functional fields | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Quadratic and bilinear Diophantine equations, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Plane and space curves Most binary forms come from a pencil of quadrics | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Kodaira-Spencer map; canonical height; relative discriminant Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for curves, Algebraic functions and function fields in algebraic geometry On the Kodaira-Spencer map and stability | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) enumerative geometry; topological Galois theory; Galois covering; monodromy; Newton polytope Coverings in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Toric varieties, Newton polyhedra, Okounkov bodies, Enumerative problems (combinatorial problems) in algebraic geometry, Multiply transitive finite groups, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Monodromy on manifolds Sparse polynomial equations and other enumerative problems whose Galois groups are wreath products | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algorithm; Heegner points Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computational aspects of algebraic curves, Number-theoretic algorithms; complexity Algorithm for computing Heegner points of \(Y_ 0(N)\) | 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 \(x^n+y^m+1=0\) value sets; finite fields; polynomials; towers of function fields Polynomials over finite fields, Algebraic functions and function fields in algebraic geometry A link between minimal value set polynomials and tamely ramified 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 curve; Picard group; Galois group; rational point Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points Rational points on Picard groups of some genus-changing curves of genus at least 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 \(x^n+y^m+1=0\) truth of abc conjecture implies truth of Mordell conjecture; Masser- Oesterlé abc-conjecture N. Elkies, \(ABC\) implies Mordell, Int. Math. Res. Notices (1991), no. 7, 99--109. Diophantine inequalities, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points \(abc\) implies Mordell | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 algebraic number fields; Nevanlinna theory; Mordell conjecture; hyperbolic geometry Rational points, Arithmetic ground fields for curves, Hyperbolic and Kobayashi hyperbolic manifolds, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, Value distribution theory in higher dimensions, Arithmetic theory of algebraic function fields Arithmetic and hyperbolic 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 \(x^n+y^m+1=0\) rational solutions of cubic Diophantine equations; complex multiplication; elliptic curves; group of endomorphisms; rational points Wajngurt, C.: Rational solutions of Diophantine equations isomorphic to elliptic curves with applications to complex multiplication. J. number theory 23, 80-85 (1986) Special algebraic curves and curves of low genus, Complex multiplication and abelian varieties, Cubic and quartic Diophantine equations, Rational points, Algebraic functions and function fields in algebraic geometry, Elliptic curves Rational solutions of Diophantine equations isomorphic to elliptic curves with applications to complex multiplication | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 continued fraction expansions; Baby-Step Giant-Step algorithm; algebro-geometric methods Arithmetic theory of algebraic function fields, Algebraic number theory computations, Applications to coding theory and cryptography of arithmetic geometry, Algebraic coding theory; cryptography (number-theoretic aspects) 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 \(x^n+y^m+1=0\) moduli space of curves; meromorphic functions; ELSV compactification; Hurwitz scheme Families, moduli of curves (algebraic), Algebraic functions and function fields in algebraic geometry, Stacks and moduli problems Polar parts and the ELSV compactification | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; Cogalois extension; torsion module; Galois extension Algebraic field extensions, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Algebraic number theory: global fields, Algebraic functions and function fields in algebraic geometry Radical extensions for the Carlitz module | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hilbert's fourteenth problem; algebra of subfinite type; graded linear series; Newton-Okounkov bodies Arithmetic varieties and schemes; Arakelov theory; heights, Curves of arbitrary genus or genus \(\ne 1\) over global fields On subfiniteness of graded linear series | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Bilinear complexity; finite fields; algebraic function fields; algebraic curves Ballet, Stéphane; Chaumine, Jean, On the bounds of the bilinear complexity of multiplication in some finite fields, Appl. Algebra Engrg. Comm. Comput., 0938-1279, 15, 3-4, 205-211, (2004) Curves over finite and local fields, Arithmetic ground fields for curves, Arithmetic theory of algebraic function fields, Number-theoretic algorithms; complexity, Finite ground fields in algebraic geometry, Analysis of algorithms and problem complexity On the bounds of the bilinear complexity of multiplication in some 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 curve; algebraic points of small degree; Mordell-Weil group; linear systems Curves of arbitrary genus or genus \(\ne 1\) over global fields, Cubic and quartic Diophantine equations, Rational points, Arithmetic ground fields for curves Algebraic points of small degree on the affine curve \(y^3=x(x-1)(x-2)(x-3)\) | 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 \(x^n+y^m+1=0\) algebraic curves; function field; automorphism group Danisman, Y.; Özdemir, M., On subfields of GK and generalized GK function fields, \textit{J. Korean Math. Soc.}, 52, 2, 225-237, (2015) Algebraic functions and function fields in algebraic geometry, Automorphisms of curves On subfields of GK and generalized GK 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 statistics; non-hyperelliptic curves; rational points; Selmer groups; Jacobians; geometry of numbers; Mumford theta groups Curves of arbitrary genus or genus \(\ne 1\) over global fields, Galois cohomology of linear algebraic groups, Asymptotic results on counting functions for algebraic and topological structures, Rational points, Global ground fields in algebraic geometry, Jacobians, Prym varieties, Special algebraic curves and curves of low genus The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 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 \(x^n+y^m+1=0\) algebraic geometric codes; algebraic curves over finite fields; function fields; Goppa codes; complexity of multiplication in extension fields; divisors of curves of genus 1; weight distributions; minimal weight Other types of codes, Geometric methods (including applications of algebraic geometry) applied to coding theory, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry Contributions to the theory of coding and complexity using 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 \(x^n+y^m+1=0\) genus-changing algebraic curves; finite number of rational points; characteristic \(p\); function field; non-conservative algebraic curve Jeong, S.: Rational points on algebraic curves that change genus. J. number theory 67, 170-181 (1998) Rational points, Algebraic functions and function fields in algebraic geometry, Special algebraic curves and curves of low genus Rational points on algebraic curves that change genus | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) hyperbolicity; Lang-Vojta conjectures; Brody hyperbolicity; logarithmic pairs; log general type Varieties over global fields, Number-theoretic analogues of methods in Nevanlinna theory (work of Vojta et al.), Hyperbolic and Kobayashi hyperbolic manifolds, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for surfaces or higher-dimensional varieties Hyperbolicity of varieties of log general type | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; genus 2 and 3; curves with many rational points Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Arithmetic ground fields for curves Algebraic curves of genus 2 and 3 having 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 \(x^n+y^m+1=0\) modular curves; elliptic curves; complex multiplication; automorphisms Elliptic curves over global fields, Complex multiplication and moduli of abelian varieties, Arithmetic aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Modular and Shimura varieties Automorphisms of Cartan modular curves of prime and composite level | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Çakçak, E.; Özbudak, F., Number of rational places of subfields of the function field of the Deligne-Lusztig curve of ree type, \textit{Acta Arith}, 120, 1, 79-106, (2005) Arithmetic theory of algebraic function fields, Curves over finite and local fields, Finite ground fields in algebraic geometry Number of rational places of subfields of the function field of the Deligne-Lusztig curve of Ree type | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Bertini; Northcott; height; abelian varieties Abelian varieties of dimension \(> 1\), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for abelian varieties Bertini and Northcott | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 curve; thin set; rational point; height; lattice; binary quadratic form Varieties over global fields, Heights, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Counting solutions of Diophantine equations, Quadratic forms over global rings and fields, Global ground fields in algebraic geometry On uniform bounds for rational points on rational curves and thin sets | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 group; Galois closure; Galois group; plane curve; uniform projection Algebraic functions and function fields in algebraic geometry, Automorphisms of curves, Plane and space curves Examples of plane 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 \(x^n+y^m+1=0\) algebraic ordinary difference equations; strong rational general solutions; parametrization; separable difference equation; resultant theory General theory of difference equations, Growth, boundedness, comparison of solutions to difference equations, Algebraic functions and function fields in algebraic geometry, Special algebraic curves and curves of low genus Rational solutions of first-order algebraic ordinary difference equations | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; function field tower; Gilbert-Varshamov bound; Garcia-Stichtenoth tower Aleshnikov, I.; Kumar, V.P.; Shum, K.W.; Stichtenoth, H., On the splitting of places in a tower of function fields meeting the Drinfeld-vlădųt bound, IEEE trans. inf. theory, 47, 4, 1613-1619, (2001) Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Bounds on codes, Arithmetic theory of algebraic function fields On the splitting of places in a tower of function fields meeting the Drinfeld-Vlăduţ 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 \(x^n+y^m+1=0\) Galois covers; rational pullback; inverse Galois theory Ramification problems in algebraic geometry, Inverse Galois theory, Arithmetic theory of algebraic function fields, Coverings in algebraic geometry, Field arithmetic, Arithmetic algebraic geometry (Diophantine geometry) Rational pullbacks of Galois 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 \(x^n+y^m+1=0\) theta functions; generalized Jacobi formula R. Salvati Manni, On Jacobi's formula in the not necessarily azygetic case, American Journal of Mathematics 108 (1986), 953--972. Theta functions and abelian varieties, Algebraic functions and function fields in algebraic geometry On Jacobi's formula in the not necessarily azygetic case | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) simple abelian variety; algebraic cycle; Lefschetz class; Tate conjecture; Fermat curve DOI: 10.1016/j.jnt.2012.09.023 Algebraic cycles, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Finite ground fields in algebraic geometry, Subvarieties of abelian varieties, Étale and other Grothendieck topologies and (co)homologies Lefschetz classes of simple factors of the Jacobian variety of a Fermat curve of prime degree 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 \(x^n+y^m+1=0\) Sato-Tate group; abelian varieties; equidistribution; Frobenius eigenvalues Curves of arbitrary genus or genus \(\ne 1\) over global fields, Transcendental methods, Hodge theory (algebro-geometric aspects), Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Galois representations Sato-Tate groups of genus 2 curves | 0 |
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