text
stringlengths 209
2.82k
| label
int64 0
1
|
|---|---|
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Pollard kangaroo method; Pollard lambda method; real quadratic function field; class number; infrastructure; parallel algorithms; discrete logarithm DOI: 10.1090/S0025-5718-01-01343-6 Number-theoretic algorithms; complexity, Algebraic number theory computations, Class numbers, class groups, discriminants, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry The parallelized Pollard kangaroo method in real quadratic 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 \(x^n+y^m+1=0\) Parshin symbol; linear group; algebraic surface; discrete valuation field Symbols and arithmetic (\(K\)-theoretic aspects), Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields A note on 2-dimensional arithmetic symbols on \(\mathrm{Gl}(n,\Sigma_S)\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; towers of function fields; asymptotically bad towers Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry Asymptotically bad towers of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) arithmetic function fields; Kähler differentials; dualizing sheaves; arithmetic schemes; elliptic curves; Fermat curves; Kähler different; valuations Kunz, E.; Waldi, R.: On Kähler's integral differential forms of arithmetic function fields. Abh. math. Sem. univ. Hamburg 73, 297-310 (2003) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields On Kähler's integral differential forms of arithmetic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) arithmetic over function fields; arithmetic of algebraic curves; Mordell Weil theorem; Mordell conjecture Rational points, Global ground fields in algebraic geometry, Arithmetic ground fields for curves, Heights, Elliptic curves over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic theory of algebraic function fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry Diophantine geometry on curves over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational functions; decomposability Fuchs, C.; Pethő, A.: Composite rational functions having a bounded number of zeros and poles. Proc. am. Math. soc. 139, No. 1, 31-38 (2011) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Composite rational functions having a bounded number of zeros and poles
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(K\)-theory; ring \(C^*\)-algebra; function field \(K\)-theory and operator algebras (including cyclic theory), Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Adèle rings and groups \(K\)-theory for ring \(C^*\)-algebras attached to function fields with only one infinite place
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; explicit equations; Selmer group; two-covering; Jacobian; Kummer surface Flynn, E. Victor; Testa, Damiano; Van Luijk, Ronald: Two-coverings of Jacobians of curves of genus 2. Proc. lond. Math. soc. (3) 104, No. 2, 387-429 (2012) Coverings of curves, fundamental group, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Jacobians, Prym varieties Two-coverings of Jacobians of curves of genus 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 \(x^n+y^m+1=0\) Kummer surface; Jacobian of genus 2 curve; twist; Brauer-Manin obstruction \(K3\) surfaces and Enriques surfaces, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points The two faces of the twisted Kummer 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 \(x^n+y^m+1=0\) modular curve; genus 2 Y. Hasegawa: Table of quotient curves of modular curves \(X_0(N)\) with genus 2. Proc. Japan Acad., 71A , 235-239 (1995). Curves of arbitrary genus or genus \(\ne 1\) over global fields, Holomorphic modular forms of integral weight, Modular and Shimura varieties Table of quotient curves of modular curves \(X_ 0(N)\) with genus 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 \(x^n+y^m+1=0\) Rational points, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computer solution of Diophantine equations Corrigendum to: ``A unique pair of triangles''
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) decidability; Hilbert's Tenth Problem; uncomputably large integral points on algebraic curves; diophantine prefix; polynomials; height bounds; geometry of complex surfaces and 3-folds J.M. Rojas, Uncomputably large integral points on algebraic plane curves?, Theoret. Comput. Sci., 235 (this Vol.) (2000) 145--162. Decidability of theories and sets of sentences, Diophantine equations in many variables, Arithmetic problems in algebraic geometry; Diophantine geometry, Decidability (number-theoretic aspects), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Curves in algebraic geometry, Rational and ruled surfaces, Undecidability and degrees of sets of sentences Uncomputably large integral points on algebraic plane curves?
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) functions with given singularities; Riemann-Roch Theorem Algebraic functions and function fields in algebraic geometry On a theorem about 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 \(x^n+y^m+1=0\) rational points; geometric quadratic Chabauty; Poincaré torsor; biextension Curves of arbitrary genus or genus \(\ne 1\) over global fields, Counting solutions of Diophantine equations, Rational points Geometric quadratic Chabauty over number fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) real curve; linear pencil; real gonality; separating gonality; Teichmüller space; special type Real algebraic and real-analytic geometry, Special divisors on curves (gonality, Brill-Noether theory), Algebraic functions and function fields in algebraic geometry Pencils on separating \((M-2)\)-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 \(x^n+y^m+1=0\) elementary functions; differential fields; algebraic curve; divisor; algorithmic integration in finite terms; algorithms; transcendental functions; algebraic functions Symbolic computation and algebraic computation, Extension theory of commutative rings, Algebraic functions and function fields in algebraic geometry, Differential algebra, Divisors, linear systems, invertible sheaves, Software, source code, etc. for problems pertaining to measure and integration, Software, source code, etc. for problems pertaining to algebraic geometry Primitives des fonctions élémentaires (d'après Risch et Davenport)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 group; abelian variety Tadashi Ochiai and Fabien Trihan, On the Selmer groups of abelian varieties over function fields of characteristic \?>0, Math. Proc. Cambridge Philos. Soc. 146 (2009), no. 1, 23 -- 43. Arithmetic ground fields for abelian varieties, Arithmetic theory of algebraic function fields On the Selmer groups of abelian varieties over function fields of characteristic \(p > 0\)
| 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 \(x^n+y^m+1=0\) higher genus curves; visualisation; Brauer-Manin obstruction; Shafarevich-Tate group A. Arnth-Jensen , E.V. Flynn , Supplement to: Non-trivial \(\Sha\) in the Jacobian of an infinite family of curves of genus 2 . Available at: http://people.maths.ox.ac.uk/flynn/genus2/af/artlong.pdf [2] N. Bruin , E.V. Flynn , Exhibiting Sha[2] on Hyperelliptic Jacobians . J. Number Theory 118 ( 2006 ), 266 - 291 . MR 2225283 | Zbl 1118.14035 Jacobians, Prym varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\), Rational points Exhibiting SHA[2] on hyperelliptic 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 \(x^n+y^m+1=0\) A. Surroca. \textit{Sur l'effectivité du théorème de Siegel et la conjecture abc}. J. Number Theory, \textbf{124} (2007), 267-290. Higher degree equations; Fermat's equation, Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Heights, Linear forms in logarithms; Baker's method Effectiveness of Siegel's theorem and the abc 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 \(x^n+y^m+1=0\) Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields, Varieties over finite and local fields, Algebraic cycles, Finite ground fields in algebraic geometry Degree 3 cohomology of function fields of 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 \(x^n+y^m+1=0\) symplectic groups; invariant subfield Chu, H.: Supplementary note on ''rational invariants of certain orthogonal and unitary groups''. Bull. London math. Soc. 29, 37-42 (1997) Transcendental field extensions, Linear algebraic groups over finite fields, Geometric invariant theory, Arithmetic theory of algebraic function fields, Group actions on varieties or schemes (quotients) Supplementary note on ``Rational invariants of certain orthogonal and unitary groups''
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Drinfeld modules; local shtukas; complex multiplication; Artin \(L\)-series Drinfel'd modules; higher-dimensional motives, etc., Zeta functions and \(L\)-functions of number fields, Arithmetic theory of algebraic function fields, Formal groups, \(p\)-divisible groups Periods of Drinfeld modules and local shtukas with 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 \(x^n+y^m+1=0\) curves of genus two; Jacobians; rational torsion subgroup; elliptic curves; table of groups Leprévost, F.; Howe, E.; Poonen, B.: Sous-groupes de torsion d'ordres élevés de jacobiennes décomposables de courbes de genre 2 (Large torsion subgroups of split Jacobians of curves of genus 2). C. R. Acad. sci. Paris sér. I math. 323, 1031-1034 (1996) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Abelian varieties of dimension \(> 1\) Large torsion subgroups of split Jacobians of curves of genus 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 \(x^n+y^m+1=0\) twists of curves; plane quartic curves; automorphism groups; Fermat quartic; Klein quartic Lorenzo García, E., Twists of non-hyperelliptic genus 3 curves, Int. J. Number Theory, 14, 06, 1785-1812, (2018) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Families, moduli of curves (algebraic), Special algebraic curves and curves of low genus, Plane and space curves Twists 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 \(x^n+y^m+1=0\) Birch-Swinnerton-Dyer conjecture; Jacobians; curves; isogeny \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Abelian varieties of dimension \(> 1\), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Isogeny The Birch and Swinnerton-Dyer conjecture for an elliptic curve over \(\mathbb{Q}(\sqrt[4]{5})\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Pagot, G.:
\[
\mathbb{F}_{p}
\]
-espaces vectoriels de formes différentielles logarithmiques sur la droite projective. J. Number Theory 97, 58--94 (2002) Structure of families (Picard-Lefschetz, monodromy, etc.), Arithmetic theory of algebraic function fields, Local structure of morphisms in algebraic geometry: étale, flat, etc. \(\mathbb F_p\)-spaces of logarithmic differential forms on the projective line.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) birational anabelian; algebraically closed fields; absolute Galois group; function fields; Galois-type correspondence Elliptic curves over global fields, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Algebraic functions and function fields in algebraic geometry A birational anabelian reconstruction theorem for curves over algebraically closed fields in arbitrary 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 of Brauer groups; rational function fields over global fields; Ulm invariants B. Fein, M.M. Schacher and J. Sonn, Brauer groups of rational function fields, Bull. Amer. Math. Soc. 1, 766-768. Arithmetic theory of algebraic function fields, Galois cohomology, Transcendental field extensions, Brauer groups of schemes Brauer groups of 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 \(x^n+y^m+1=0\) Laumon, G.: Cohomology of Drinfeld Modular Varieties. Part II: Automorphic Forms, Trace Formulas and Langlands Correspondences. Cambridge Studies in Advanced Mathematics Cambridge University Press, Cambridge (2009) Modular and Shimura varieties, Drinfel'd modules; higher-dimensional motives, etc., Global ground fields in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Arithmetic theory of algebraic function fields, Formal groups, \(p\)-divisible groups, Research exposition (monographs, survey articles) pertaining to number theory Cohomology of Drinfeld modular varieties. Part II: Automorphic forms, trace formulas and Langlands correspondence. With an appendix by Jean-Loup Waldspurger
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois theory; specializations; \(abc\)-conjecture; Malle conjecture; uniformity conjecture; hyperelliptic and superelliptic curves; rational points; twisted covers; Hasse principle Galois theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Coverings in algebraic geometry, Rational points Density results for specialization sets 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 \(x^n+y^m+1=0\) rational ruled surface; meromorphic functions; Jacobian; invariant image curve; reduction theorem Meromorphic functions of several complex variables, Algebraic functions and function fields in algebraic geometry Families of complex analytic curves and meromorphic mappings of Poincaré of several complex variables
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Conference; Seattle, WA (USA); Galois problem; Inverse Galois problem Michael D. Fried, Shreeram S. Abhyankar, Walter Feit, Yasutaka Ihara, and Helmut Voelklein , Recent developments in the inverse Galois problem, Contemporary Mathematics, vol. 186, American Mathematical Society, Providence, RI, 1995. Papers from the Joint Summer Research Conference held at the University of Washington, Seattle, Washington, July 17 -- 23, 1993. Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to field theory, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Inverse Galois theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Coverings of curves, fundamental group Recent developments in the inverse Galois problem. A joint summer research conference, July 17-23, 1993, University of Washington, Seattle, WA, USA
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) integral points on algebraic curves; rational point; Jacobian; linear form of logarithms; Mordell-Weil group; height Hirata-Kohno N. , Une relation entre les points entiers sur une courbe algébrique et les points rationnels de la jacobienne , in: Advances in Number Theory , Kingston, ON, 1991 , Oxford University Press , New York , 1993 , pp. 421 - 433 . MR 1368438 | Zbl 0805.14009 Rational points, Arithmetic ground fields for abelian varieties, Linear forms in logarithms; Baker's method, Curves of arbitrary genus or genus \(\ne 1\) over global fields A relation between integral points on algebraic curves and rational points of 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 \(x^n+y^m+1=0\) zeta-function Curves over finite and local fields, Rational points, Arithmetic theory of algebraic function fields Algebraic curves over finite fields with many rational points
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) local-global obstruction; rational points; hyperelliptic curves; descent A.~Petho, On the solution of the equation \(G_n=P(x)\). In \textit{Fibonacci numbers and their applications (Patras, 1984)}, vol.~28 of \textit{Math. Appl.}, (Reidel, Dordrecht, 1986) pp. 193-201 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Computer solution of Diophantine equations, Jacobians, Prym varieties Two-cover descent on 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 \(x^n+y^m+1=0\) Galois point; genus-one curve; Galois group Kanazawa, M; Yoshihara, H, Galois group at Galois point for genus-one curve, Int. J. Algebra, 5, 1161-1174, (2011) Elliptic curves, Algebraic functions and function fields in algebraic geometry, Elliptic curves over global fields, Automorphisms of curves Galois group at Galois point for genus-one 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 \(x^n+y^m+1=0\) Hindes, Wade, Prime divisors in polynomial orbits over function fields, Bull. Lond. Math. Soc., 48, 6, 1029-1036, (2016) Algebraic functions and function fields in algebraic geometry, Galois theory, Rational points, Arithmetic ground fields for curves, Arithmetic dynamics on general algebraic varieties Prime divisors in polynomial orbits 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 \(x^n+y^m+1=0\) distinct distances; algebraic curves; incidences; symmetries of curves Pach, J., Zeeuw, F. de.: Distinct distances on algebraic curves in the plane. Comb. Probab. Comput. (to appear) Erdős problems and related topics of discrete geometry, Combinatorial complexity of geometric structures, Algebraic functions and function fields in algebraic geometry Distinct distances on algebraic curves in the plane
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 curve; tetragonal Arithmetic aspects of modular and Shimura varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves Tetragonal 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 \(x^n+y^m+1=0\) cyclic covers of the projective line; Weierstrass points; total Weierstrass weight C. Towse, ''Weierstrass Points on Cyclic Covers of the Projective Line,'' Trans. Am. Math. Soc. 348, 3355--3378 (1996). Riemann surfaces; Weierstrass points; gap sequences, Curves of arbitrary genus or genus \(\ne 1\) over global fields Weierstrass points on cyclic covers of the projective line
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 ground fields for curves, Étale and other Grothendieck topologies and (co)homologies, Algebraic functions and function fields in algebraic geometry On residue maps for affine 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 \(x^n+y^m+1=0\) Tate constant; hypergeometric differential equation; Legendre family of elliptic curves; Tate curve; Picard-Fuchs equation; Hasse-Witt matrix; formal group Local ground fields in algebraic geometry, Families, moduli of curves (algebraic), Algebraic functions and function fields in algebraic geometry, Formal groups, \(p\)-divisible groups, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions) On the Tate-matrix
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Drinfeld modules; torsion points; Manin-Mumford conjecture Ghioca, D.; Hsia, L.-C., Torsion points in families of Drinfeld modules, Acta Arith., 161, 219-240, (2013) Drinfel'd modules; higher-dimensional motives, etc., Algebraic functions and function fields in algebraic geometry, Elliptic curves Torsion points in families of 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 \(x^n+y^m+1=0\) Drinfeld modules; Tate algebras; de Rham map; uniformizability Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Difference algebra, Krasner-Tate algebras, de Rham cohomology and algebraic geometry The de Rham isomorphism for Drinfeld modules over Tate 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 \(x^n+y^m+1=0\) continued fraction expansion; function field of characteristic zero; hyperelliptic curve; Somos sequence A.\ J. van der Poorten, ``Hyperelliptic curves, continued fractions, and Somos sequences'', Dynamics \(\&\) Stochastics, Lecture Notes--Monograph Series, v. 48, ed. Denteneer, Dee and Hollander, Frank den and Verbitskiy, Evgeny, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006, 212--224 Continued fractions, Elliptic curves over global fields, Algebraic functions and function fields in algebraic geometry, Elliptic curves Hyperelliptic curves, continued fractions, and Somos sequences
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) absolute logarithmic height of an algebraic number; number of points of bounded height lying on an algebraic plane curve W. M. Schmidt, Heights of algebraic points lying on curves or hypersurfaces , Proc. Amer. Math. Soc. 124 (1996), no. 10, 3003-3013. JSTOR: Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves Heights of algebraic points lying on curves or hypersurfaces
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Arakelov theory; Arakelov-Green functions; Wronskian differential; Belyi degree; arithmetic surfaces; Riemann surfaces; curves; Arakelov invariants; Faltings height; discriminant; faltings' delta invariant; self-intersection of the dualising sheaf; branched covers Javanpeykar, A.: Polynomial bounds for Arakelov invariants of Belyi curves. With an appendix by Peter Bruin. Algebra Number Theory \textbf{8}(1), 89-140 (2014) Arithmetic varieties and schemes; Arakelov theory; heights, Dessins d'enfants theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic aspects of dessins d'enfants, Belyĭ theory, Heights, Riemann surfaces; Weierstrass points; gap sequences, Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems Polynomial bounds for Arakelov invariants of Belyi curves. With an appendix by Peter Bruin.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) zeta-function; number-field; finiteness of Brauer group; function-field analogue of the conjecture of Birch and Swinnerton-Dyer Lichtenbaum, S.: Behavior of the zeta-function of open surfaces at s=1. Adv. stud. Pure math. 17, 271-287 (1989) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Global ground fields in algebraic geometry, Arithmetic theory of algebraic function fields Behavior of the zeta-function of open surfaces at \(s=1\)
| 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 \(x^n+y^m+1=0\) abelian functions; theta functions H. F. Baker, \textit{Abelian Functions: Abel's Theorem and the Allied Theory of Theta Functions} (Cambridge Univ. Press, Cambridge, 1995). Algebraic functions and function fields in algebraic geometry, Theta functions and curves; Schottky problem, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Theta functions and abelian varieties Abelian functions. Abel's theorem and the allied theory of theta functions. Foreword by Igor Krichever (xvii-xxx).
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Chowla-Zassenhaus conjecture; cyclic polynomial; \(p\)th Chebyshev polynomial; extension of constants; branch cycle; Davenport polynomials Fried M D. Extension of Constants, Rigidity, and the Chowla-Zassenhaus Conjecture. Finite Fields Appl, 1995, 1: 326--359 Galois theory, Separable extensions, Galois theory, Coverings in algebraic geometry, Arithmetic theory of algebraic function fields Extension of constants, rigidity, and the Chowla-Zassenhaus 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 \(x^n+y^m+1=0\) monodromy; branched coverings; Riemann surfaces; fundamental group; Galois theory Riemann surfaces; Weierstrass points; gap sequences, Coverings of curves, fundamental group, Algebraic functions and function fields in algebraic geometry, Classification theory of Riemann surfaces Note on the deck transformations group and the monodromy group
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cubic arcs; Galois planes Blocking sets, ovals, \(k\)-arcs, Algebraic functions and function fields in algebraic geometry On cubic arcs of a Galois plane of odd order
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; elliptic curves; Jacobian; Weierstrass points; rank; quartic Martine Girard, Géométrie du groupe des points de Weierstrass d'une quartique lisse, J. Number Theory 94 (2002), no. 1, 103 -- 135 (French, with English and French summaries). Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Special algebraic curves and curves of low genus, Riemann surfaces; Weierstrass points; gap sequences Geometry of the group of Weierstrass points of a smooth quartic
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Jacobians, Prym varieties, Coverings of curves, fundamental group, Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields Erratum to: Hyperelliptic curves with prescribed \(p\)-torsion
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 reciprocity; function fields; theta function; Gauss sums K. Merrill and H. Walling, On quadratic reciprocity over function fields, Pacific J. Math. 173 (1996), 147--150. Arithmetic theory of algebraic function fields, Power residues, reciprocity, Theta functions and abelian varieties, Gauss and Kloosterman sums; generalizations On quadratic reciprocity 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 \(x^n+y^m+1=0\) transformation of order 3; Pappian plane; algebraic curve Desarguesian and Pappian geometries, Homomorphism, automorphism and dualities in linear incidence geometry, Algebraic functions and function fields in algebraic geometry Transformations of order 3 between two Pappian projective 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 \(x^n+y^m+1=0\) algebraic function fields; constructions of linear codes; algebraic curves; algebraic-geometric codes; Goppa codes Ferruh Özbudak and Henning Stichtenoth, Constructing codes from algebraic curves, IEEE Trans. Inform. Theory 45 (1999), no. 7, 2502 -- 2505. Geometric methods (including applications of algebraic geometry) applied to coding theory, Linear codes (general theory), Arithmetic theory of algebraic function fields, Applications to coding theory and cryptography of arithmetic geometry Constructing codes from 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 \(x^n+y^m+1=0\) \(p\)-torsion of the Jacobian variety; Galois module structure Arithmetic theory of algebraic function fields, Integral representations related to algebraic numbers; Galois module structure of rings of integers, Jacobians, Prym varieties \(p\)-adic Galois representation of the Jacobian variety
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Goppa codes; divisors of curves; Riemann-Roch theorem; linear codes Michon, J. F.: Codes de goppa. Sem. th. Nombres Bordeaux 7 (1983--1984) Linear codes (general theory), Algebraic functions and function fields in algebraic geometry, Divisors, linear systems, invertible sheaves Codes de Goppa
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) pro-\(\ell \) fundamental group; ramification; Galois action; branched coverings Anderson, GW; Ihara, Y., Pro-\(l\) branched coverings of \({ P}^1\) and higher circular \(l\)-units. II, Int. J. Math., 1, 119-148, (1990) Coverings of curves, fundamental group, Arithmetic theory of algebraic function fields, Coverings in algebraic geometry Pro-\(\ell\) branched coverings of \({\mathbb{P}}^ 1\) and higher circular \(\ell\)-units. 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 \(x^n+y^m+1=0\) rationality; locus of a conic Algebraic functions and function fields in algebraic geometry, Rational and unirational varieties A note on Ohm's rationality criterion for conics
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 field; number field; curve over a finite field; class number; regulator; discriminant bound; explicit formulae; infinite global field; Brauer-Siegel theorem Tsfasman, M. A.; Vlăduţ, S. G., Infinite global fields and the generalized Brauer--Siegel theorem\upshape, Dedicated to Yuri I. Manin on the occasion of his 65th birthday, Mosc. Math. J., 2, 2, 329-402, (2002) Curves over finite and local fields, Zeta functions and \(L\)-functions of number fields, Class field theory, Rational points, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry Infinite global fields and the generalized Brauer-Siegel 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 \(x^n+y^m+1=0\) algebraic curves; field of moduli; field of definition Coverings of curves, fundamental group, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves A simple remark on fields of definition
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Beilinson's conjecture; tame symbol; regulator Liu, Hang; de Jeu, Rob, On \(K_2\) of certain families of curves, Int. Math. Res. Not. IMRN, 21, 10929-10958, (2015) Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Polylogarithms and relations with \(K\)-theory On \(K_{2}\) of certain families 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 \(x^n+y^m+1=0\) reciprocity law; Steinberg symbol; algebraic curve; finite covering Symbols and arithmetic (\(K\)-theoretic aspects), Algebraic functions and function fields in algebraic geometry An explicit reciprocity law associated to some finite coverings of algebraic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) periodic points; algebraic function; 2-adic field; ring class fields; quartic Fermat equation 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. I.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves over finite fields; Jacobian; torsion points; Weil pairing; Hilbert symbol E. W. Howe, The Weil pairing and the Hilbert symbol. Mathematische Annalen 305 (1996), 387-392. Zbl0854.11031 MR1391223 Curves over finite and local fields, Class field theory, Arithmetic theory of algebraic function fields, Arithmetic ground fields for curves The Weil pairing and the Hilbert symbol
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; Mordell-Weil rank; Jacobian variety Families, moduli of curves (algebraic), Jacobians, Prym varieties, Pencils, nets, webs in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields On Néron's construction of curves with high rank. 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 \(x^n+y^m+1=0\) arithmetic fundamental group; moduli space of curves; Galois group over Q Galois theory, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Curves over finite and local fields, Inverse Galois theory, Coverings of curves, fundamental group The Grothendieck-Teichmüller group and Galois theory of the rational numbers -- European network GTEM
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 curve; twist; Mordell-Weil rank; Jacobian Jędrzejak, T.; Top, J.; Ulas, M.: Tuples of hyperelliptic curves y2=xn+a, Acta arith. 150, No. 2, 105-113 (2011) Curves of arbitrary genus or genus \(\ne 1\) over global fields, Special algebraic curves and curves of low genus Tuples of hyperelliptic curves \(y^2=x^n+a\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Proceedings, conferences, collections, etc. pertaining to number theory, Abelian varieties of dimension \(> 1\), Curves over finite and local fields, Varieties over finite and local fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic coding theory; cryptography (number-theoretic aspects), Special algebraic curves and curves of low genus, Arithmetic ground fields for abelian varieties, Representations of finite groups of Lie type, Geometric methods (including applications of algebraic geometry) applied to coding theory, Proceedings of conferences of miscellaneous specific interest Arithmetic, geometry, cryptography and coding theory, AGC2T, 17th international conference, Centre International de Rencontres Mathématiques, Marseilles, France, June 10--14, 2019
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic functions BLISS G. A., Algebraic Functions (1966) Algebraic functions and function fields in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry Algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) non-standard analysis; algebraic field theory; group theory Nonstandard models in mathematics, Nonstandard arithmetic and field theory, Algebraic functions and function fields in algebraic geometry Algebraic function fields and non-standard analysis
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mordell's equation; characteristic three VOLOCH (J.F.) . - Mordell's equation in characteristic three , Bull. Austral. Math. Soc., t. 41, 1990 , p. 149-150. MR 91b:11072 | Zbl 0698.14017 Finite ground fields in algebraic geometry, Cubic and quartic Diophantine equations, Arithmetic theory of algebraic function fields Mordell's equation in characteristic three
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves of genus 2; Mordell-Weil group; Mordell-Weil rank; rational points; absolutely simple Jacobian; high rank Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties Examples of genus 2 curves over \(\mathbb{Q}\) with Jacobians of high Mordell-Weil 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 \(x^n+y^m+1=0\) automorphism group; positive characteristic; Artin-Schreier curves Automorphisms of curves, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry An elementary abelian \(p\)-cover of the Hermitian curve with many 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 \(x^n+y^m+1=0\) DOI: 10.1016/S0377-0427(03)00624-1 Curves of arbitrary genus or genus \(\ne 1\) over global fields, Elliptic curves over global fields, Arithmetic ground fields for curves Some families of Mordell curves associated to cubic 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 \(x^n+y^m+1=0\) noncommutative formal power series; language; zeta function; algebraic function C. Kassel and C. Reutenauer, Complete determination of the zeta function of the Hilbert scheme of n points on a two-dimensional torus, \textit{Ramanujan J.}, to appear. Noncommutative algebraic geometry, Exact enumeration problems, generating functions, Algebraic theory of languages and automata, Combinatorics on words, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Algebraicity of the zeta function associated to a matrix over a free group algebra
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; hyperelliptic curves; Tate modules; Galois groups Yuri G. Zarhin, Galois groups of Mori trinomials and hyperelliptic curves with big monodromy, European J. Math., DOI 10.1007/s40879-015-0048-2. Jacobians, Prym varieties, Algebraic theory of abelian varieties, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Abelian varieties of dimension \(> 1\) Galois groups of Mori trinomials and hyperelliptic curves with big monodromy
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) periods of integrals on Mumford curve L. Gerritzen , Integrale zweiter Gattung auf Mumfordkurven , Math. Ann. 270 ( 1985 ), 381 - 392 . MR 774363 | Zbl 0535.14016 Arithmetic ground fields for curves, Local ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Special algebraic curves and curves of low genus Integrale zweiter Gattung auf Mumfordkurven
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) genera of functions fields; rigid geometry Matignon, M.; Youssefi, T.: Appendix to inégalité relative des genres by T. Youssefi. Manuscripta math. 78, No. 2, 111-128 (1993) Algebraic functions and function fields in algebraic geometry, Valuations and their generalizations for commutative rings, Curves over finite and local fields, Local ground fields in algebraic geometry Relative inequality between genera. Appendix by Michel Matignon and Taoufik Youssefi: Good reduction and surjective morphisms
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mordell--Weil rank; Selmer group; Jacobians; curves over global fields; Shafarevich--Tate group; descent; Galois cohomology B. Poonen and E. Schaefer, ''Explicit Descent for Jacobians of Cyclic Covers of the Projective Line,'' J. Reine Angew. Math. 488, 141--188 (1997). Curves of arbitrary genus or genus \(\ne 1\) over global fields, Jacobians, Prym varieties, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for curves Explicit descent for Jacobians of cyclic covers of the projective line
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) holomorphic family; function field; Kodaira surface; Teichmüller space; Diophantine equation; Riemann surfaces; holomorphic section Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Families, moduli of curves (analytic), Curves of arbitrary genus or genus \(\ne 1\) over global fields, Teichmüller theory for Riemann surfaces A remark on holomorphic sections of certain holomorphic families of 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 \(x^n+y^m+1=0\) deformations of curve; cyclic cover of projective line; period space for Riemann surfaces; holomorphic differentials; group of automorphisms Coverings of curves, fundamental group, Families, moduli of curves (algebraic), Differentials on Riemann surfaces, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Algebraic functions and function fields in algebraic geometry, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) The geometry of the period mapping on cyclic covers of \({\mathbb{P}}_ 1\)
| 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 \(x^n+y^m+1=0\) Functional determinant; curve; taqngent Curves in algebraic geometry, Algebraic functions and function fields in algebraic geometry On functions that behave similar to functional determinants.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) generalized algebraic geometry codes; n-automorphisms; admissible function fields; Hermitian function fields A. Picone, Automorphisms of generalized algebraic geometry codes, Ph.D. Thesis, Università degli Studi di Palermo, 2007 Algebraic functions and function fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory Automorphisms of Hermitian generalized 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 \(x^n+y^m+1=0\) Archimedean real closed field; function field; fibration; Hasse principle; Severi-Brauer varieties Fibrations, degenerations in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Semialgebraic sets and related spaces, Other nonalgebraically closed ground fields in algebraic geometry Fibration in Severi-Brauer varieties above the projective line over the function field of a real 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 \(x^n+y^m+1=0\) Riemann-Roch theorem; algebraic function fields Algebraic functions and function fields in algebraic geometry Eine Vorbereitung auf den Riemann-Rochschen Satz für algebraische Funktionenkörper
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Algebraic functions of one variable. Research exposition (monographs, survey articles) pertaining to algebraic geometry, Algebraic functions and function fields in algebraic geometry The theory of algebraic functions of one variable and their application to algebraic curves and abelian 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 \(x^n+y^m+1=0\) simple Lie algebras; McKay correspondence; Vogel's universality; Diophantine equations; regular maps Khudaverdian, H.M.; Mkrtchyan, R.L., Diophantine equations, platonic solids, mckay correspondence, equivelar maps and Vogel's universality, J. geom. phys., 114, 85-90, (2017) Cubic and quartic Diophantine equations, Curves of arbitrary genus or genus \(\ne 1\) over global fields, McKay correspondence, Simple, semisimple, reductive (super)algebras, Three-dimensional polytopes Diophantine equations, platonic solids, McKay correspondence, equivelar maps and Vogel's universality
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) valuation; residue field extension; Gauss extension; rational function field; algebraic function field; genus zero; quaternion algebra Valued fields, Transcendental field extensions, General valuation theory for fields, Algebraic functions and function fields in algebraic geometry, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) A ruled residue theorem for function fields of conics
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 of functions; uniqueness polynomial; functional equation Algebraic functions and function fields in algebraic geometry, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, Riemann surfaces; Weierstrass points; gap sequences Heights of function field points on curves given by equations with separated variables
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) modular forms; Hecke algebra; modular curves; elliptic curves; Jacobian Zeng, J.; Yin, L., On the computation of coefficients of modular forms: the reduction modulo \textit{p} approach, Math. Comp., 84, 1469-1488, (2015) Fourier coefficients of automorphic forms, Curves over finite and local fields, Number-theoretic algorithms; complexity, Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry On the computation of coefficients of modular forms: the reduction modulo \(p\) 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 \(x^n+y^m+1=0\) polynomials; divisors; partitions of integers; pseudo-geometric sequences Polynomials over finite fields, Algebraic functions and function fields in algebraic geometry Un problème de diviseurs dans \({\mathbb F}_q[X]\). (A divisor problem in \({\mathbb F}_q[X])\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) elliptic curves; torsion subgroup; rationals; quadratic fields González-Jiménez, Enrique; Tornero, José M., Torsion of rational elliptic curves over quadratic fields II, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 110, 1, 121-143, (2016) Elliptic curves over global fields, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points Torsion of rational elliptic curves over quadratic fields. 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 \(x^n+y^m+1=0\) positive characteristic; Chevalley-Weil formula; group action on smooth curve; space of regular differentials on curve; first cohomology group G. Ellingsrud, On the representation afforded by the space of regular differentials of a group acting freely on a curve in characteristic \(p\) , Preprint, Stockholm, 1983. Algebraic functions and function fields in algebraic geometry, Group actions on varieties or schemes (quotients), Finite ground fields in algebraic geometry On the representation afforded by the space of regular differentials of a group acting freely on a curve 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 \(x^n+y^m+1=0\) genus 2 curve; Jacobian; isogeny; Magma tool P.B. van Wamelen, Computing with the analytic Jacobian of a genus 2 curve, in W. Bosma, J. Cannon, M. Bronstein, A.M. Cohen, H. Cohen, D. Eisenbud, B. Sturmfels, editors, \textit{Discovering Mathematics with Magma}. Algorithms and Computation in Mathematics, vol. 19 (Springer, Berlin Heidelberg, 2006), pp. 117-135 Computational aspects of algebraic curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic ground fields for curves, Computational number theory Computing with the analytic Jacobian of a genus 2 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 \(x^n+y^m+1=0\) Arakelov divisor; effectivity; theta divisor; Riemann-Roch G. Van Der Geer , R. Schoof , Effectivity of Arakelov Divisors and the Theta Divisor of a Number Field . Preprint 1999 , version 3. URL: '' http://xxx.lanl.gov/abs/math/9802121 '' . arXiv | MR 1847381 Arithmetic theory of algebraic function fields, Arithmetic varieties and schemes; Arakelov theory; heights, Zeta functions and \(L\)-functions of number fields Effectivity of Arakelov divisors and the theta divisor of a 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 \(x^n+y^m+1=0\) Coresolvents; integralization; rational function; entire function; algebraic function; differential quotient; multilinear solution; system of \(n\) homogeneous quadratic equations; unknowns; differential equations Algebraic functions and function fields in algebraic geometry, Real rational functions, Equations in general fields, Multilinear algebra, tensor calculus, Implicit ordinary differential equations, differential-algebraic equations, Research exposition (monographs, survey articles) pertaining to real functions, Continuity and differentiation questions Third Chapter on Coresolvents.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 of one variable over finite fields; Gauss sum; non- polynomial class {\#}1 rings Thakur D. : Gauss sums for function fields , J. Number Theory 37 (1991) 242-252. Arithmetic theory of algebraic function fields, Other character sums and Gauss sums, Drinfel'd modules; higher-dimensional motives, etc., Finite ground fields in algebraic geometry Gauss sums for function fields
| 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.