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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 \(x^n+y^m+1=0\) conjecture of Lang and Silverman; absolute height; abelian surfaces; local height Pazuki, F., \textit{minoration de la hauteur de Néron-Tate sur LES surfaces abéliennes}, Manuscripta Math., 142, 61-99, (2013) Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\) Lower bound of the Néron-Tate height on abelian 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 \(x^n+y^m+1=0\) Néron-Tate height; Deligne-Mumford stratification; semi-stable curve Local ground fields in algebraic geometry, Heights, Algebraic functions and function fields in algebraic geometry, Families, moduli of curves (algebraic), Arithmetic varieties and schemes; Arakelov theory; heights Uniform bound for the effective Bogomolov 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 \(x^n+y^m+1=0\) elementary equivalence; isomorphism; isogeny; function field; Severi-Brauer variety; quadric; elliptic curve; Jacobian Transcendental field extensions, Quadratic forms over general fields, Elliptic curves over global fields, Arithmetic theory of algebraic function fields, Model theory of fields, Grassmannians, Schubert varieties, flag manifolds, Brauer groups (algebraic aspects) On elementary equivalence, isomorphism and isogeny
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) local Pfister conjecture; fields of rational functions Finite-dimensional division rings, Quadratic forms over general fields, Forms over real fields, Brauer groups (algebraic aspects), Skew fields, division rings, Algebraic functions and function fields in algebraic geometry, Rational and ruled surfaces Quaternionicity of \(\Omega\)-algebras with special ramification.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Tadokoro Y. (2006). The pointed harmonic volumes of hyperelliptic curves with Weierstrass base points. Kodai Math. J. 29(3): 370--382 Algebraic functions and function fields in algebraic geometry, Special algebraic curves and curves of low genus, Riemann surfaces; Weierstrass points; gap sequences The pointed harmonic volumes of hyperelliptic curves with Weierstrass base 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 \(x^n+y^m+1=0\) four-sheeted covering of a sphere Coverings of curves, fundamental group, Vector spaces, linear dependence, rank, lineability, Algebraic functions and function fields in algebraic geometry An effective construction of an algebraic function field corresponding to a four-sheeted covering of a sphere and 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; Carlitz zeta function; Bernoulli numbers; gamma function; p-adic zeta function D.S. Thakur Number fields and function fields (zeta and gamma functions at all primes), p-adic analysis , Proc. Conf. Houthalen/Belg ( 1986 ), 149 - 157 . MR 921867 | Zbl 0658.12005 Arithmetic theory of algebraic function fields, Quaternion and other division algebras: arithmetic, zeta functions, Class field theory, Zeta functions and \(L\)-functions of number fields, Langlands-Weil conjectures, nonabelian class field theory, Zeta functions and \(L\)-functions, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite fields and commutative rings (number-theoretic aspects) Number fields and function fields. (Zeta and gamma functions at all primes)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; function fields; arithmetic duality, Galois cohomology Izquierdo, D., Variétés abéliennes sur les corps de fonctions de courbes sur des corps locaux, Doc. Math., 22, 297-361, (2017) Arithmetic ground fields for abelian varieties, Geometric class field theory, Rational points, Algebraic functions and function fields in algebraic geometry, Galois cohomology, Étale and other Grothendieck topologies and (co)homologies, Local ground fields in algebraic geometry Abelian varieties for function fields of curves over local 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 \(x^n+y^m+1=0\) sums of squares; hereditarily Pythagorean fields; hereditarily Euclidean fields; Pythagoras number; u-invariant Becher K.J., Van Geel J.: Sums of squares in function fields of hyperelliptic curves. Math. Z. 209, 829--844 (2009) Sums of squares and representations by other particular quadratic forms, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Algebraic functions and function fields in algebraic geometry Sums of squares in function fields 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 \(x^n+y^m+1=0\) pseudofinite field; isogeny; Tate pairing associated to an isogeny Isogeny, Algebraic functions and function fields in algebraic geometry, Abelian varieties of dimension \(> 1\) On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite 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 \(x^n+y^m+1=0\) quadratic function field; quadratic number field; ideal class group; algorithm; Jacobian; hyperelliptic curve; concordant ideals; g-adic numbers; elliptic function fields; elliptic curves; 2-descent Hellegouarch, Y.: Algorithme pour calculer LES puissances successives d'une classe d'idéaux dans uns corps quadratique. Application aux courbes elliptiques. C. R. Acad. sci. Paris sér. I 305, 573-576 (1987) Quadratic extensions, Arithmetic theory of algebraic function fields, Elliptic curves, Software, source code, etc. for problems pertaining to field theory, Jacobians, Prym varieties, Higher degree equations; Fermat's equation, Algebraic number theory: local fields Algorithme pour calculer les puissances successives d'une classe d'idéaux dans un corps quardatique. Application aux courbes elliptiques. (An algorithm for computing the successive powers of an ideal class in the quadratic field. Application to elliptic 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 \(x^n+y^m+1=0\) coverings of curves; descent; method of Chabauty Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Jacobians, Prym varieties Cycles 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 \(x^n+y^m+1=0\) rational points; Jacobians; curves of higher genus; descent; Mordell-Weil group Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Jacobians, Prym varieties Solving diophantine problems on curves via descent on the Jacobian
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) S. Rybakov, ''Zeta functions of conic bundles and Del Pezzo surfaces of degree 4 over finite fields,'' Mosc. Math. J. 5(4), 919--926 (2005). Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Zeta and \(L\)-functions in characteristic \(p\), Rational points Zeta functions of conic bundles and del Pezzo surfaces of degree 4 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 \(x^n+y^m+1=0\) Litsyn S., Rains E.M., Sloane N.J.A.: Table of nonlinear binary codes online table at http://www.eng.tau.ac.il/~litsyn/tableand/. Accessed Sept 2014. Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Algebraic functions and function fields in algebraic geometry New binary codes from 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 \(x^n+y^m+1=0\) genus 2 curves; \(K3\) surfaces; Tate-Shafarevich group; Brauer-Manin obstruction G. A. Corn and T. M. Corn, \textit{Mathematical Handbook for Scientists and Engineers} (McGraw-Hill, New York, 1961). Jacobians, Prym varieties, Abelian varieties of dimension \(> 1\), Global ground fields in algebraic geometry, \(K3\) surfaces and Enriques surfaces, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Varieties over global fields Tate-Shafarevich groups and \(K3\) 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 \(x^n+y^m+1=0\) abelian variety; function fields of curves; heights; Néron model Varieties over global fields, Elliptic curves over global fields, Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields Torsion sections of abelian fibrations
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) C. Consani and M. Marcolli, ''Spectral triples from Mumford curves,'' Int. Math. Research Notices 36, 1945--1972 (2003). Curves of arbitrary genus or genus \(\ne 1\) over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Local ground fields in algebraic geometry, Symbolic dynamics, Noncommutative dynamical systems, Noncommutative global analysis, noncommutative residues Spectral triples from Mumford 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 \(x^n+y^m+1=0\) central division algebras; cyclic algebras; ramification; curve points; nodal points; Brauer groups; curves over local fields; \(p\)-adic curves; field extensions; algebraic function fields; curves over rings of integers of \(p\)-adic fields D. J. Saltman, ''Cyclic algebras over \(p\)-adic curves,'' J. Algebra, vol. 314, iss. 2, pp. 817-843, 2007. Finite-dimensional division rings, Curves over finite and local fields, Arithmetic ground fields for curves, Brauer groups of schemes, Skew fields, division rings, Algebras and orders, and their zeta functions, Algebraic functions and function fields in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Local ground fields in algebraic geometry, Special surfaces Cyclic algebras over \(p\)-adic curves.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational points on curves; Chabauty's method; étale descent Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Computer solution of Diophantine equations Explicit two-cover descent for 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 \(x^n+y^m+1=0\) arithmetic divisor group; intersection pairing; forms; currents; Green's functions; non-Archimedean places; Arakelov pairing [13]R. Rumely, A new equivariant in nonarchimedean dynamics, in preparation. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Global ground fields in algebraic geometry, Arithmetic ground fields for curves An intersection pairing for curves, with analytic contributions from nonarchimedean 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 \(x^n+y^m+1=0\) modular towers; inverse Galois problem Fried, M.D., Kopeliovich, Y.: Applying modular towers to the inverse Galois problem. In: Geometric Galois Actions, 2. London Math. Soc. Lecture Note Ser., vol. 243, pp. 151--175. Cambridge University Press, Cambridge (1997) Inverse Galois theory, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Arithmetic theory of algebraic function fields Applying modular towers to the inverse Galois 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 \(x^n+y^m+1=0\) ÇakÇak, E; Özbudak, F, Some Artin-Schreier type function fields over finite fields with prescribed genus and number of rational places, J. Pure Appl. Algebra, 210, 113-135, (2007) Curves over finite and local fields, Arithmetic theory of algebraic function fields, Rational points, Finite ground fields in algebraic geometry Some Artin-Schreier type function fields over finite fields with prescribed genus and number of 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 \(x^n+y^m+1=0\) Brauer group; rational function field Quaternion and other division algebras: arithmetic, zeta functions, Brauer groups of schemes, Galois cohomology, Arithmetic theory of algebraic function fields On the separable part of the Brauer group of the field of rational functions of one variable with a global field of constants
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curve singularity; Alexander polynomial Antonio Campillo, Félix Delgado & Sabir M. Gusein-Zade, ``The Alexander polynomial of a plane curve singularity via the ring of functions on it'', Duke Math. J.117 (2003) no. 1, p. 125-156 Global theory of complex singularities; cohomological properties, Algebraic functions and function fields in algebraic geometry, Singularities of curves, local rings The Alexander polynomial of a plane curve singularity via the ring of functions on it
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) crystalline cohomology; zeta function; hyperelliptic curve; rigid cohomology \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, \(p\)-adic cohomology, crystalline cohomology, de Rham cohomology and algebraic geometry, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Curves of arbitrary genus or genus \(\ne 1\) over global fields Galois representations associated to smooth 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 \(x^n+y^m+1=0\) Dyson's theorem; integral points on curves; Siegel's theorem; diophantine approximation on curves Curves of arbitrary genus or genus \(\ne 1\) over global fields, Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for curves Dyson's theorem for 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 \(x^n+y^m+1=0\) Picard curves; discriminant; conductor Families, moduli of curves (algebraic), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Plane and space curves Conductor and discriminant of Picard 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 cover of curves; weakly ramified; epsilon constant; equivariant Euler characteristic Arithmetic theory of algebraic function fields, Integral representations related to algebraic numbers; Galois module structure of rings of integers, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Coverings of curves, fundamental group Galois-module theory for wildly ramified covers of curves over finite fields (with an appendix by Bernhard Köck and Adriano Marmora)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) weak approximation; global function fields; local-global criteria Rational points, Arithmetic theory of algebraic function fields Weak approximation for points with coordinates in rank-one subgroups of global function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves; automorphism groups; \(p\)-rank Automorphisms of curves, Algebraic functions and function fields in algebraic geometry Large automorphism groups of ordinary 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 \(x^n+y^m+1=0\) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Global ground fields in algebraic geometry, Special algebraic curves and curves of low genus Generalized explicit descent and its application to 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 \(x^n+y^m+1=0\) central simple algebras; Henselian fields; quaternion algebras; conic bundle surfaces; real closed fields; ramification; Fadeev reciprocity law Finite-dimensional division rings, Quadratic forms over general fields, Forms over real fields, Brauer groups (algebraic aspects), Skew fields, division rings, Algebraic functions and function fields in algebraic geometry, Rational and ruled surfaces \(\Omega\)-algebras over Henselian discrete valued fields with real closed residue field.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves; rational points; genus; linear codes; asymptotics; tower of curves Arnaldo Garcia, On curves over finite fields, Arithmetic, geometry and coding theory (AGCT 2003), Sémin. Congr., vol. 11, Soc. Math. France, Paris, 2005, pp. 75 -- 110 (English, with English and French summaries). Finite ground fields in algebraic geometry, Arithmetic ground fields for curves, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Rational points On curves over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) KP equation; canonical form of matrices; Kadomtsev-Petviashvili; Riemann theta function; Riemann matrix; Schottky problem; period matrix Segur, H.; Finkel, A.: Basic form for Riemann matrices. Lectures in applied mathematics 23 (1986) Period matrices, variation of Hodge structure; degenerations, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Partial differential equations of mathematical physics and other areas of application, Algebraic functions and function fields in algebraic geometry, Compact Riemann surfaces and uniformization Basic form for Riemann matrices
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Weierstraß points Martine Girard, Groupe des points de Weierstrass sur une famille de quartiques lisses, Preprint, December 1999. Riemann surfaces; Weierstrass points; gap sequences, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus Group of Weierstrass points on a family of smooth quartics.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) 1-cohomology set; Shafarevich set T. Ono: On Shafarevich-Tate sets. Proc. The 7th MSJ Int. Res. Inst. Class Field Theory-its centenary and prospect (to appear). Galois cohomology, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Automorphisms of curves On Shafarevich-Tate 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 \(x^n+y^m+1=0\) Miura K.: Galois points on singular plane quartic curves. J. Algebra 287, 283--293 (2005) Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory, Plane and space curves, Singularities of curves, local rings Galois points on singular plane quartic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) higher genus curves; Jacobians; Tate-Shafarevich group Flynn, EV, Descent via (5,5)-isogeny on Jacobians of genus 2 curves, J. Number Theory, 153, 270-282, (2015) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Jacobians, Prym varieties Descent via \((5, 5)\)-isogeny on Jacobians of 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 \(x^n+y^m+1=0\) Hasse principle; genus 2; algebraic curves; Jacobian; Mordell-Weil rank Bremner, A.: Some interesting curves of genus 2 to 7. J. Number Theory 67, 277-290 (1997) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus, Jacobians, Prym varieties Some interesting curves of genus 2 to 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 \(x^n+y^m+1=0\) quadratic polynomial; dynamical arboreal representation; Hall-Lang conjecture; rational points on curves Hindes, W., The arithmetic of curves defined by iteration, Acta Arith., 169, 1-27, (2015) Rational points, Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps, Separable extensions, Galois theory, Dynamical systems over global ground fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves over global fields, Special algebraic curves and curves of low genus, Groups acting on trees, Arithmetic dynamics on general algebraic varieties, Arithmetic ground fields for curves The arithmetic of curves defined by iteration
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) upper half plane; arithmetic groups; Fricke involution; genus Kim, C.H., Koo, J.K.: Estimation of genus for certain arithmetic groups. Commun. Algebra 32(7), 2479--2495 (2004) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Riemann surfaces; Weierstrass points; gap sequences Estimation of genus for certain arithmetic 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 \(x^n+y^m+1=0\) Fermat curves; Hurwitz-Klein curves; low degree points; Chabauty-Coleman's method Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves Improved bounds on the number of low-degree points on certain 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 \(x^n+y^m+1=0\) Chabauty; Coleman; Jacobian; divisor; abelian integral; Mordell-Weil sieve; generalized Fermat; rational points Siksek S., Explicit Chabauty over number fields, Algebra Number Theory 7 (2013), no. 4, 765-793. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Analytic theory of abelian varieties; abelian integrals and differentials, Divisors, linear systems, invertible sheaves Explicit 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 \(x^n+y^m+1=0\) computation of the conductor; projective points Computational aspects of algebraic curves, Analysis of algorithms and problem complexity, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Algebraic functions and function fields in algebraic geometry A remark on the computation of the Hilbert function applied to the conductor of 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 \(x^n+y^m+1=0\) continued fractions; fundamental units; \(S\)-units; torsion in the Jacobians; hyperelliptic fields; divisors; divisor class group Curves of arbitrary genus or genus \(\ne 1\) over global fields, Continued fractions, Jacobians, Prym varieties, Special algebraic curves and curves of low genus On families of hyperelliptic curves over the field of rational numbers, whose Jacobian contains torsion points of given orders
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Tzermias, P, Low-degree points on Hurwitz-Klein curves, Trans. Am. Math. Soc., 356, 939-951, (2003) Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points Low-degree points on Hurwitz-Klein 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 \(x^n+y^m+1=0\) Goppa codes; designed minimum distance, floor of a divisor Güneri, C.; Stichtenoth, H.; Taşkın, \.I.: Further improvements on the designed minimum distance of algebraic geometry codes. J. pure appl. Algebra 213, No. 1, 87-97 (2009) Applications to coding theory and cryptography of arithmetic geometry, Algebraic functions and function fields in algebraic geometry Further improvements on the designed minimum distance of algebraic geometry codes
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finite field; maximal curve; Suzuki curve; Weierstrass semigroup; Weierstrass points Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences Weierstrass semigroups on the Skabelund maximal 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 \(x^n+y^m+1=0\) Selmer sets; average size; plane quartic; genus 3; rational points; family; hyperflex Rational points, Group actions on varieties or schemes (quotients), Curves of arbitrary genus or genus \(\ne 1\) over global fields \(E_{6}\) and the arithmetic 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 \(x^n+y^m+1=0\) Chabauty; Coleman; curves; Jacobian; symmetric powers; divisors; differentials; abelian integrals Siksek, S, Chabauty for symmetric powers of curves, Algebra Number Theory, 3, 209-236, (2009) 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 Chabauty for symmetric powers 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 \(x^n+y^m+1=0\) Diophantine geometry; fundamental group; Diophantine decidability Kim, M.: Remark on fundamental groups and effective Diophantine methods for hyperbolic curves. In: Goldfeld, D. et al. (eds.) Number Theory, Analysis and Geometry, pp. 355-368. Springer, New York (2012) (http://people.maths.ox.ac.uk/kimm/papers/effective.pdf) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves Remark on fundamental groups and effective Diophantine methods for hyperbolic 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 \(x^n+y^m+1=0\) rational points; curves; Chabauty; nonabelian; quadratic; geometric Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields Geometric quadratic Chabauty
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) specialization; algebraic covers; twisting lemma; Hilbert's irreducibility theorem; Grunwald's problem; PAC fields; local fields; global fields; Hurwitz spaces Dèbes, Pierre and Legrand, François Specialization results in Galois theory Trans. Amer. Math. Soc.365 (2013) 5259--5275 Math Reviews MR3074373 Coverings of curves, fundamental group, Arithmetic theory of algebraic function fields, Field arithmetic, Rational points Specialization results in Galois theory
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) heights; Jacobian variety; hyperelliptic curve E. V. Flynn, An explicit theory of heights , Trans. Amer. Math. Soc. 347 (1995), no. 8, 3003-3015. JSTOR: Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties An explicit theory of heights
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 reciprocity law; arithmetic elliptic function field; automorphism group; Jacobi function of level N; Jacobi forms Arithmetic theory of algebraic function fields, Theta series; Weil representation; theta correspondences, Arithmetic ground fields (finite, local, global) and families or fibrations, Automorphic functions in symmetric domains La loi de réciprocité de Shimura pour les fonctions de Jacobi
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) polynomial equations of genus zero and one; function field; algorithms; effective determination; diophantine equations in two unknowns; Thue equations; hyperelliptic equations; fundamental inequality; fields of positive characteristic; explicit bounds; solutions in rational functions; superelliptic equations R. C. Mason, \textit{Diophantine Equations over Function Fields.} London Mathematical Society Lecture Note Series, Vol. 96. Cambridge Univ. Press, Cambridge, 1984. \(p\)-adic and power series fields, Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic theory of algebraic function fields, Exponential Diophantine equations, Diophantine equations, Approximation to algebraic numbers, Higher degree equations; Fermat's equation, Rational points Diophantine equations over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curve; moduli; rationality Algebraic functions and function fields in algebraic geometry, Special algebraic curves and curves of low genus On the rationality of certain Weierstrass spaces of type \((5, g)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Laplace's equation; Cayley-Bacharach theorem; cohomology of sheaves Projective techniques in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Integral representations of solutions to PDEs Geometric methods in partial differential 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 \(x^n+y^m+1=0\) Siegel's theorem; unipotent representation; torsors; monodromy; unipotent bundles G. Faltings, Mathematics around Kim's new proof of Siegel's theorem, Diophantine Goemetry, Proceedings of the research program at the Centro di Ricerca Matematica Ennio de Giorgi, U. Zannier (ed.), 390 pp., 2007. Curves of arbitrary genus or genus \(\ne 1\) over global fields, Étale and other Grothendieck topologies and (co)homologies, Arithmetic problems in algebraic geometry; Diophantine geometry Mathematics around Kim's new proof of Siegel'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 \(x^n+y^m+1=0\) modular curves; class numbers; elliptic curves Chen, I, On siegel's modular curve of level 5 and the class number one problem, J. Number Theory, 74, 278-297, (1999) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Class numbers, class groups, discriminants, Elliptic curves over local fields, Modular and Shimura varieties On Siegel's modular curve of level 5 and the class number one 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 \(x^n+y^m+1=0\) universal deformation of formal module; Galois character Keating, K. : Galois extensions associated to deformations of formal A-modules , J. Fac. Sci. Univ. Tokyo 37 (1990) 151-170. Formal groups, \(p\)-divisible groups, Class field theory; \(p\)-adic formal groups, Formal power series rings, Arithmetic theory of algebraic function fields Galois extensions associated to deformations of formal A-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 \(x^n+y^m+1=0\) finite fields; polynomials; curves with many points Lenstra, H. W., On a problem of garcia, stichtenoth, and Thomas, Finite Fields Appl., 8, 166-170, (2002) Curves over finite and local fields, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields On a problem of Garcia, Stichtenoth, and Thomas.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(\mathbb{Q}\)-curves; \(j\)-invariants; hyperelliptic modular curves; Chabauty method Elliptic curves over global fields, Holomorphic modular forms of integral weight, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Modular and Shimura varieties, Arithmetic aspects of modular and Shimura varieties Hyperelliptic parametrizations of \(\pmb{\mathbb{Q}}\)-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 \(x^n+y^m+1=0\) transcendence; zeta-function; period; algebraic function field; Drinfeld module; modular function Jing Yu, Transcendence and Drinfel\(^{\prime}\)d modules, Invent. Math. 83 (1986), no. 3, 507 -- 517. Transcendence theory of Drinfel'd and \(t\)-modules, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Formal groups, \(p\)-divisible groups Transcendence and Drinfeld modules
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois point; plane curve; positive characteristic; Galois group Fukasawa, S., Complete determination of the number of Galois points for a smooth plane curve, Rend. Semin. Mat. Univ. Padova, 129, 93-113, (2013) Plane and space curves, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry Complete determination of the number of Galois points for a smooth plane 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 \(x^n+y^m+1=0\) Hyperelliptic curves; p-ranks, wild ramification, automorphisms of curves DOI: 10.1142/S1793042109002468 Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Automorphisms of curves The 2-ranks of hyperelliptic curves with extra automorphisms
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 discriminant; Vojta's inequality; height; morphisms of curves Curves of arbitrary genus or genus \(\ne 1\) over global fields, Diophantine inequalities, Rational points, Global ground fields in algebraic geometry, Heights, Arithmetic varieties and schemes; Arakelov theory; heights, Arithmetic ground fields for curves Arithmetic discriminants and morphisms 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 \(x^n+y^m+1=0\) Grothendieck-Katz \(p\)-curvature conjecture Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rigid analytic geometry, Fibrations, degenerations in algebraic geometry The \(p\)-curvature conjecture and monodromy around simple closed loops
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 conjecture; machine-learning; classifiers; \(L\)-functions; hyper-elliptic curves \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computational number theory, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Learning and adaptive systems in artificial intelligence Machine-learning the Sato-Tate 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 \(x^n+y^m+1=0\) Galois point; positive characteristic; plane curve Fukasawa S.: On the number of Galois points for a plane curve in positive characteristic II. Geom. Dedicata. 127, 131--137 (2007) Plane and space curves, Coverings of curves, fundamental group, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry On the number of Galois points for a plane curve in positive characteristic. 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 \(x^n+y^m+1=0\) K-theory; function field; elliptic curve; motivic cohomology Arithmetic theory of algebraic function fields, Elliptic curves over global fields, Motivic cohomology; motivic homotopy theory, Whitehead groups and \(K_1\), Steinberg groups and \(K_2\), Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects) First and second \(K\)-groups of an elliptic curve over a global field 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 \(x^n+y^m+1=0\) curves over global fields; local-global principle; nice variety Poonen, B.: Curves over every global field violating the local-global principle. Zap. Nauchn. Sem. POMI \textbf{377} (2010), Issledovaniya po Teorii Chisel \textbf{10}, 141-147, 243-244. Reprinted in: J. Math. Sci. (N.Y.) \textbf{171}, 782-785 (2010) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points Curves over every global field violating the local-global 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 \(x^n+y^m+1=0\) elliptic curves; torsion points; hyperelliptic curves; torsion packets Elliptic curves over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Special algebraic curves and curves of low genus, Elliptic curves Elliptic curves with common torsion \(x\)-coordinates and hyperelliptic torsion packets
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Drinfel'd modules; higher-dimensional motives, etc., Geometric class field theory, Langlands-Weil conjectures, nonabelian class field theory, Arithmetic theory of algebraic function fields, Algebraic moduli problems, moduli of vector bundles, Étale and other Grothendieck topologies and (co)homologies, \(p\)-adic cohomology, crystalline cohomology, Other transforms and operators of Fourier type, Local ground fields in algebraic geometry A new Fourier transform
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 of rational points; varieties over function fields; cardinaltiy of the set of fibrations; uniform boundedness of rational points; distribution of rational points Enumerative problems (combinatorial problems) in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Families, moduli of curves (algebraic), Rational points Remarks about uniform boundedness of rational points 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 \(x^n+y^m+1=0\) canonical height; hyperelliptic curve; curve of genus 2; Jacobian surface; Kummer surface J.S. Müller, M. Stoll, Canonical heights on genus two Jacobians. Algebra & Number Theory 10(10), 2153-2234 (2016) Heights, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Arithmetic varieties and schemes; Arakelov theory; heights, Computational aspects of algebraic curves, Rational points Canonical heights on genus-2 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 \(x^n+y^m+1=0\) number fields, function fields Shafarevich, I.R.: Algebraic number fields. In: Proc. Internat. Congr. Mathematicians (Stockholm, 1962), pp. 163-176. Inst. Mittag-Leffler, Djursholm (1963) Research exposition (monographs, survey articles) pertaining to field theory, Arithmetic theory of algebraic function fields, Algebraic number theory: local fields, Research exposition (monographs, survey articles) pertaining to algebraic geometry Algebraic number 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 \(x^n+y^m+1=0\) stable reduction of the Fermat curve Arithmetic ground fields for curves, Global theory and resolution of singularities (algebro-geometric aspects), Special algebraic curves and curves of low genus, Global ground fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Singularities of surfaces or higher-dimensional varieties Resolution of surface singularities and stable reduction of 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 \(x^n+y^m+1=0\) plane curves; Poncelet type property; quadratic extension Algebraic functions and function fields in algebraic geometry, Plane and space curves Hyperelliptic algebraic function field associated with certain contraction.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) square values of quadratic polynomials; covering collections; elliptic Chabauty method González-Jiménez, E.; Xarles, X., On symmetric square values of quadratic polynomials, Acta Arith., 149, 2, 145-159, (2011) Counting solutions of Diophantine equations, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves On symmetric square values of quadratic polynomials
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) deformation of symmetric product of curves; hyperelliptic curve Families, moduli of curves (algebraic), Algebraic moduli problems, moduli of vector bundles, Algebraic functions and function fields in algebraic geometry, Special algebraic curves and curves of low genus Symmetric products 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 \(x^n+y^m+1=0\) algebraic curves; nonstandard analysis; asymptotical directions; asymptotes; paramatrisation Nonstandard analysis, Algebraic functions and function fields in algebraic geometry, Plane and space curves On the asymptotic behaviour of cubics. (Sur le comportement asymptotique des cubiques.)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 approximation; system of formal equations; algebroid curve Local deformation theory, Artin approximation, etc., Algebraic functions and function fields in algebraic geometry, Formal power series rings, Étale and flat extensions; Henselization; Artin approximation A note on the one-dimensional systems of formal 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 \(x^n+y^m+1=0\) canonical height; curves of genus two; rational torsion; Jacobian Stoll, M., On the height constant for curves of genus two, Acta Arith., 90, 2, 183-201, (1999) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus, Heights, Jacobians, Prym varieties, Arithmetic varieties and schemes; Arakelov theory; heights, Abelian varieties of dimension \(> 1\) On the height constant for curves of genus two
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Bogomolov conjecture over function fields; discrete embedding of curve; Néron-Tate height pairing; admissible pairing; Green function; semistable arithmetic surface A. Moriwaki, Bogomolov conjecture over function fields for stable curves with only irreducible fibers, Compos. Math. 105 (1997), 125-140. Algebraic functions and function fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Picard groups Bogomolov conjecture over function fields for stable curves with only irreducible fibers
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 of genus greater than one Leveque, W. J.: Rational points on curves of genus greater than 1. J. reine angew math. 206, 45-52 (1961) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points Rational points on curves of genus greater than 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 \(x^n+y^m+1=0\) binary field with many rational places; global function field Niederreiter, H., Xing, C.P.: Explicit global function fields over the binary field with many rational places. Acta Arithm.~75, 383--396 (1996) Arithmetic theory of algebraic function fields, Curves over finite and local fields, Finite ground fields in algebraic geometry Explicit global function fields over the binary field with many rational places
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) computer algebra; polynomial factorization; reducible curves; function fields; divisors; algebraic extensions Duval D (1991) Absolute factorization of polynomials: a geometric approach. SIAM J Comput 20:1--21 Symbolic computation and algebraic computation, Polynomials in real and complex fields: factorization, Algebraic functions and function fields in algebraic geometry, Divisors, linear systems, invertible sheaves, Algebraic field extensions Absolute factorization of polynomials: A geometric approach
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 with rank \(\geq 12\); curves over function fields Jean-François Mestre, Courbes elliptiques de rang \ge 12 sur \?(\?), C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 4, 171 -- 174 (French, with English summary). Elliptic curves over global fields, Elliptic curves, Arithmetic theory of algebraic function fields Elliptic curves with rank \(\geq 12\) over \(\mathbb Q(t)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) special divisors; theta characteristics; trigonal curves Special algebraic curves and curves of low genus, Algebraic functions and function fields in algebraic geometry, Special divisors on curves (gonality, Brill-Noether theory), Divisors, linear systems, invertible sheaves Theta characteristics in trigonal 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 \(x^n+y^m+1=0\) function fields; plane cubics of genus one; exceptional points Nagell, T. Les points exceptionnels sur les cubiques planes du premier genre II, Nova Acta Reg. Soc. Sci. Ups., Ser. IV, vol 14, n:o 3, Uppsala 1947. Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences Les points exceptionnels sur les cubiques planes du premier genre. 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 \(x^n+y^m+1=0\) \(S\)-units; hyperelliptic curves; Jacobians of curves Arledge, J., \textit{S}-units attached to genus 3 hyperelliptic curves, J. Number Theory, 63, 12-29, (1997) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties \(S\)-units attached to 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 \(x^n+y^m+1=0\) parabolic connection; moduli space; compactification; Picard group Algebraic moduli problems, moduli of vector bundles, Picard groups, Algebraic functions and function fields in algebraic geometry Line bundles on the moduli space of parabolic connections over a compact Riemann surface
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Corvaja, P.; Zannier, U., On the number of integral points on algebraic curves, Journal für die reine und angewandte Mathematik, 565, 27-42, (2003) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Diophantine inequalities, Global ground fields in algebraic geometry On the number of integral points on 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 \(x^n+y^m+1=0\) Selmer groups; twists; abelian varieties; Jacobians of curves; hyperelliptic curves; superelliptic curves Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for abelian varieties Selmer ranks of twists of hyperelliptic curves and superelliptic 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 \(x^n+y^m+1=0\) infrastructures; giant steps; number fields; function fields; Riemann-Roch spaces; fundamental units F. Fontein, Holes in the infrastructure of global hyperelliptic function fields, preprint Algebraic number theory computations, Algebraic functions and function fields in algebraic geometry, Units and factorization, Class groups and Picard groups of orders The infrastructure of a global field of arbitrary unit rank
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Cartier operator; non-hyperelliptic curves; effective divisors Divisors, linear systems, invertible sheaves, Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials A bound on the genus of a curve with Cartier operator of small rank
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) covering surface; algebraic function field; Riemann problem Compact Riemann surfaces and uniformization, Algebraic functions and function fields in algebraic geometry Construction of an equation of a Riemann surface given in form of a three-sheeted covering surface of a sphere
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) p-adic ground field; elliptic curve; hyperalgebra; global analytic p-adic function Local ground fields in algebraic geometry, \(p\)-adic differential equations, Algebraic functions and function fields in algebraic geometry, Affine algebraic groups, hyperalgebra constructions Congruences by means of elliptic integrals
| 0 |
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