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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 \(x^n+y^m+1=0\) pro-\(\ell \) fundamental group; rational function field; maximum pro-\(\ell \) extension; absolute Galois group; Frobenius automorphism Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry, Galois theory On the action of the Frobenius automorphism on the pro-\(\ell\) fundamental 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 \(x^n+y^m+1=0\) translations of classics (algebraic geometry); history of algebraic geometry; mathematics of the 19th century; algebraic functions; function fields; algebraic curves; Riemann-Roch theorem; algebraic differential 2.R. Dedekind, H. Weber, \(Theory of algebraic functions of one variable.\) Translated from the 1882 German original and with an introduction, bibliography and index by John Stillwell. History of Mathematics, 39. American Mathematical Society (Providence, RI; London Mathematical Society, London, 2012), pp. viii+152 History of algebraic geometry, Biographies, obituaries, personalia, bibliographies, Algebraic functions and function fields in algebraic geometry, History of mathematics in the 19th century, Arithmetic theory of algebraic function fields, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials Theory of algebraic functions of one variable. Transl. from the German and introduced by John Stillwell
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 theorem of algebraic function fields; L-function of Galois covering of curves; function-field; characteristic polynomial of the Hasse-Witt matrix; generalised Hasse-Witt invariants Cyclotomic function fields (class groups, Bernoulli objects, etc.), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Galois theory Class groups and \(L\)-series of congruence 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 \(x^n+y^m+1=0\) irreducible curve; rational function; number of prime divisors Pappalardi, F.; Shparlinski, I.: On Artin's conjecture over function fields. Finite fields appl. 1, 399-404 (1995) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields On Artin's conjecture 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 \(x^n+y^m+1=0\) Mordell-Weil ranks; elliptic surface; Néron model L. Fastenberg, Computing Mordell-Weil ranks of cyclic covers of elliptic surfaces , Proc. Amer. Math. Soc. 129 (2001), 1877-1883. JSTOR: Rational points, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Elliptic curves over global fields, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields Computing Mordell-Weil ranks of cyclic covers of elliptic surfaces
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function field; degree one place; divisor class group Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields, Class groups A note on divisor class groups of degree zero of algebraic function fields over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Suzuki curve; Weierstrass semigroups; algebraic-geometric codes Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences Weierstrass semigroups at every point of the Suzuki 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 \(x^n+y^m+1=0\) abstract elliptic function fields; structure of ring of meromorphisms; Riemann Hypothesis Hasse, H.: Zur Theorie der abstrakten elliptischen Funktionenkörper III. Die Struktur des Meromorphismenrings. Die Riemannsche Vermutung. J. Reine Angew. Math. \textbf{175}, 193-208 (1936) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Zur Theorie der abstrakten elliptischen Funktionenkörper. III: Die Struktur des Meromorphismenringes. Die Riemannsche Vermutung
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; class group Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry Fiber products and class groups of hyperelliptic curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) elliptic Drinfeld modules; transcendence over function fields; transcendental period; exponential function; algebraic function fields Arithmetic theory of algebraic function fields, Global ground fields in algebraic geometry, Approximation in non-Archimedean valuations, Discontinuous groups and automorphic forms, Algebraic functions and function fields in algebraic geometry Transcendence of analytic parameters of rational elliptic 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 \(x^n+y^m+1=0\) maximal curves over finite fields; maximal function field H. Stichtenoth and C.P. Xing. The genus of maximal function fields over finite fields. Manuscripta Math., 86(2) (1995), 217--224. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Special algebraic curves and curves of low genus The genus of maximal function fields over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism groups; cancellation problem for function fields; function fields of general type; Zariski problem Relevant commutative algebra, Surfaces and higher-dimensional varieties, Transcendental field extensions, Algebraic functions and function fields in algebraic geometry, Group actions on varieties or schemes (quotients), Arithmetic theory of algebraic function fields Automorphism groups of ruled functions fields and a problem of Zariski
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 number fields; algebraic function fields; algebraic \(p\)-adic height pairing; elliptic curve; Selmer group; complex multiplication; pairing of Galois cohomology groups; Poincaré group; Galois extension Galois theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On a Galois extension with restricted ramification related to the Selmer group of an elliptic curve 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 \(x^n+y^m+1=0\) non-abelian L-series; holomorphic continuation D. Goss, On the holomorphy on certain nonabelian \(L\)-series , Math. Ann. 272 (1985), no. 1, 1-9. Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry On the holomorphy on certain non-Abelian L-series
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; cyclic Galois extensions; integral closures; maximal orders; Galois groups Algebraic number theory computations, Arithmetic theory of algebraic function fields, Galois theory, Class field theory, Number-theoretic algorithms; complexity, Algebraic functions and function fields in algebraic geometry Algorithms for Galois extensions of global function fields. (Abstract of thesis)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) elliptic curves over global fields; arithmetic function fields; sheaves of differentials; Kähler differentials; arithmetic schemes; valuation rings Kunz, E.; Waldi, R.: Integral differentials of elliptic function fields. Abh. math. Sem. univ. Hamburg 74, 243-252 (2004) Elliptic curves over global fields, Arithmetic theory of algebraic function fields, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Algebraic functions and function fields in algebraic geometry, Valuation rings Integral differentials of elliptic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) isomorphism of Witt rings; Witt equivalence of fields; global field; algebraic function field Koprowski, Przemysław, Local-global principle for Witt equivalence of function fields over global fields, Colloq. Math., 91, 2, 293-302, (2002) Algebraic theory of quadratic forms; Witt groups and rings, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Quadratic forms over general fields, Algebraic functions and function fields in algebraic geometry Local-global principle for Witt equivalence of function fields over global fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finite field; Hasse-Weil bound; permutation; rational function Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Polynomials over finite fields, Algebraic functions and function fields in algebraic geometry Rational functions of degree four that permute the projective line over a finite field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) square-free values of polynomials; density Distribution of integers with specified multiplicative constraints, Primes represented by polynomials; other multiplicative structures of polynomial values, Applications of sieve methods, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On square-free values of large polynomials over the rational function field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function fields defined over finite field; class number; lower bounds [BR]S. Ballet and R. Rolland, Lower bounds on the class number of algebraic function fields defined over any finite field, J. Th\'{}eor. Nombres Bordeaux 24 (2012), 505-- 540. Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry Lower bounds on the class number of algebraic function fields defined over any finite field
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function fields; algebraic curves; Riemann-Roch theorem; coding theory; algebraic-geometry codes; differentials; towers of functions fields; Tsfasman-Vladut-Zink theorem; trace codes Stichtenoth, H., \textit{Algebraic Function Fields and Codes}, 254, (2009), Springer, Berlin Algebraic functions and function fields in algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory, Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects) Algebraic function fields and 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 \(x^n+y^m+1=0\) curve; finite field; Tate pairing; Chebotarev density theorem F. Heß, A note on the Tate pairing of curves over finite fields. Archiv der Mathematik 82 (2004), no. 1, 28-32. Zbl1051.11030 MR2034467 Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Computational aspects of algebraic curves, Cryptography A note on the Tate pairing of 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 \(x^n+y^m+1=0\) archimedean absolute values; Eisenstein constant; construction of bases; Riemann-Roch space; divisor; function field of a plane curve; height; degree; non-archimedean absolute values; Puiseux series Schmidt, W.M.: Construction and estimation of bases in function fields. J. Number Theory 39, 181--224 (1991) Arithmetic theory of algebraic function fields, Algebraic number theory: local fields, Algebraic functions and function fields in algebraic geometry Construction and estimation of bases in function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) compactification of orbit space; arithmetic group; genus of algebraic curve over finite field Wolfgang Radtke, Diskontinuierliche arithmetische Gruppen im Funktionenkörperfall, J. Reine Angew. Math. 363 (1985), 191 -- 200 (German). Arithmetic ground fields for curves, Arithmetic theory of algebraic function fields, Structure of modular groups and generalizations; arithmetic groups, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Kleinian groups (aspects of compact Riemann surfaces and uniformization), Group actions on varieties or schemes (quotients), Fuchsian groups and their generalizations (group-theoretic aspects) Diskontinuierliche arithmetische Gruppen im Funktionenkörperfall. (Discontinuous arithmetic groups in case of function field)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; genus Lewittes, J, Genus and gaps in function fields, J. Pure Appl. Algebra, 58, 29-44, (1989) Arithmetic theory of algebraic function fields, Transcendental field extensions, Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields Genus and gaps in function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) multiplicator ring; elliptic function fields Deuring, M., Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Univ. Hamburg, 14, 1, 197-272, (1941) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Die Typen der Multiplikatorenringe elliptischer 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 \(x^n+y^m+1=0\) valued function fields; existence of regular functions; Henselian constant field; divisor reduction map; divisor group; elementary class Green, B.; Matignon, M.; Pop, F.: On valued function fields II: Regular functions and elements with the uniqueness property. J. reine angew. Math. 412, 128-149 (1990) Valued fields, Algebraic functions and function fields in algebraic geometry, Model theory of fields, Arithmetic theory of algebraic function fields, Field extensions On valued function fields. II: Regular functions and elements with the uniqueness property
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 modular towers; Drinfeld modules; elliptic curves; class number Drinfel'd modules; higher-dimensional motives, etc., Algebraic functions and function fields in algebraic geometry, Families, moduli of curves (algebraic), Arithmetic theory of algebraic function fields, Computational aspects of algebraic curves Good families of Drinfeld 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 \(x^n+y^m+1=0\) inertia structure; abelian-by-central Galois theory F. Pop, {\mathbb{Z}/} abelian-by-central Galois theory of prime divisors, The arithmetic of fundamental groups. Pia 2010, Contrib. Math. Comput. Sci. 2, Springer, Berlin (2011), 225-244. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry \(\mathbb{Z}\slash\ell\) abelian-by-central Galois theory of prime divisors
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) absolute irreducibility; finite field; Hasse-Weil bound; permutation; rational function Arithmetic theory of algebraic function fields, Polynomials over finite fields, Equations in general fields, Algebraic functions and function fields in algebraic geometry On a type of permutation rational functions over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field of one variable; irrationality of curve; Weierstrass divisor; Lüroth semigroup; dominant map Moh, TT; Heinzer, W, On the Lüroth semigroup and Weierstrass canonical divisor, J. Algebra, 77, 62-73, (1982) Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences, Divisors, linear systems, invertible sheaves, Arithmetic theory of algebraic function fields, Special algebraic curves and curves of low genus On the Lüroth semigroup and Weierstrass canonical divisors
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational places; class field tower; narrow ray class field Arithmetic theory of algebraic function fields, Class field theory, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry A counterexample to Perret's conjecture on infinite class field towers for 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 \(x^n+y^m+1=0\) transformation formula; Hecke operators Rosson, Holly J.: Theta series of quaternion algebras over function fields, J. number theory 94, No. 1, 49-79 (2002) Theta series; Weil representation; theta correspondences, Other groups and their modular and automorphic forms (several variables), Hecke-Petersson operators, differential operators (several variables), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Theta series of quaternion algebras over function fields.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields of conics; Zariski problem; transcendental extension; rationality; regular function field; Amitsur-MacRae theorem Jack Ohm, Function fields of conics, a theorem of Amitsur-MacRae, and a problem of Zariski, Algebraic geometry and its applications (West Lafayette, IN, 1990) Springer, New York, 1994, pp. 333 -- 363. Transcendental field extensions, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields Function fields of conics, a theorem of Amitsur-MacRae, and a problem of Zariski
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field; multiple zeta function; multiple polylogarithms Multiple Dirichlet series and zeta functions and multizeta values, Other Dirichlet series and zeta functions, Arithmetic theory of algebraic function fields, Arithmetic theory of polynomial rings over finite fields, Algebraic functions and function fields in algebraic geometry Multiple zeta functions and polylogarithms over global function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function fields Villa Salvador, G.D.: Topics in the Theory of Algebraic Function Fields. Mathematics: Theory & Applications. Birkhäuser, Boston (2006) Research exposition (monographs, survey articles) pertaining to number theory, Arithmetic theory of algebraic function fields, Galois theory, Algebraic functions and function fields in algebraic geometry, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Drinfel'd modules; higher-dimensional motives, etc. Topics in the theory of algebraic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mordell-Weil lattice; elliptic curve over function field of rank 8; rational points generating the Mordell-Weil group Elliptic curves, Rational points, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Elliptic curves over global fields, Arithmetic varieties and schemes; Arakelov theory; heights Construction of elliptic curves over \(\mathbb{Q}(t)\) with high rank: A preview
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) number of Galois extensions with isomorphic Galois group and fixed discriminant; density of discriminants of abelian extensions of global fields; asymptotic properties; class field theory; Dirichlet series Iwasawa theory, Cyclotomic extensions, Arithmetic theory of algebraic function fields, Asymptotic results on counting functions for algebraic and topological structures, Class field theory, Global ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Density theorems Distribution of discriminants of abelian extensions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Kummer function fields; Artin-Schreier function fields; different divisor; genus Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry A note on the bound of Castelnuovo's inequality
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Baker's theorem; Newton polygon; Newton polytope; Castelnuovo's inequality; Riemann-Roch space Beelen, P.: A generalization of Baker's theorem. Finite Fields Appl. 15(5), 558--568 (2009) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry A generalization of Baker'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 \(x^n+y^m+1=0\) fields of algebraic functions; matrix Riemann boundary problem; Riemann surface Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences, Arithmetic theory of algebraic function fields Construction of normal bases of rings of integral elements of certain fields of algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finite fields; Lang-Weil bound; permutations; rational function fields Arithmetic theory of algebraic function fields, Polynomials over finite fields, Arithmetic theory of polynomial rings over finite fields, Algebraic functions and function fields in algebraic geometry On a conjecture on permutation rational functions over finite fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function; radicals Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields On algebraic functions, which can be expressed in terms of radicals.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphisms; survey; Riemann surfaces; algebraic function fields; Kummer extensions Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Automorphisms of algebraic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Units and factorization, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Decomposition of places in dihedral and cyclic quintic trinomial extensions of global fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois coverings of projective non-singular algebraic curves; characteristic p.; Hasse-Witt invariant; Cartier operator; L-series Rück, H. G.: Class groups and thel-series of function fields. J. number theory 22, 177-189 (1986) Coverings of curves, fundamental group, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory, Arithmetic theory of algebraic function fields Class groups and L-series of function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curve; differentials; perfect field; solvable; tower Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Holomorphic differentials of certain solvable covers of the projective line over a perfect 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 functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Valued fields, Class field theory; \(p\)-adic formal groups Genus and residual genus of valued function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field of a curve; ultrametric valuation; function fields of surfaces; absolute values of a field; product formula; infinite extensions Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Valued fields Arithmetic on infinite extensions 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 \(x^n+y^m+1=0\) Noguchi Y (2004) Optimal properties of conditional adaptive strategies. Mimeo., Kanto Gakuin University Algebraic functions and function fields in algebraic geometry, Picard-type theorems and generalizations for several complex variables, Arithmetic ground fields for abelian varieties, Arithmetic theory of algebraic function fields, Divisors, linear systems, invertible sheaves Intersection multiplicities of holomorphic and algebraic curves with divisors
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On elementary abelian \(p\)-extensions with null Hasse-Witt map
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hasse-Witt invariant; algebraic function field; L-function Kodama, T.; Washio, T., A family of hyperelliptic function fields with Hasse-Witt invariant zero, J. Number Theory, 36, 187-200, (1990) Arithmetic theory of algebraic function fields, Curves over finite and local fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Algebraic functions and function fields in algebraic geometry A family of hyperelliptic function fields with Hasse-Witt-invariant zero
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois point; plane curve; Galois group; automorphism group Plane and space curves, Algebraic functions and function fields in algebraic geometry, Automorphisms of curves, Curves over finite and local fields, Arithmetic theory of algebraic function fields A birational embedding with two Galois points for quotient 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 \(x^n+y^m+1=0\) genus change; algebraic function fields; inseparable constant extension Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry An invariant of certain fields 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 \(x^n+y^m+1=0\) cyclotomic function field; Carlitz module; class number; Maillet determinant formula DOI: 10.1090/S0002-9939-97-03748-9 Class numbers, class groups, discriminants, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Drinfel'd modules; higher-dimensional motives, etc. A note on the relative class number in function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finite automorphism group; divisor theory; function fields Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Classification of equations with given finite automorphism group of function fields of genus 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 \(x^n+y^m+1=0\) function field; height; morphism; preperiod point Benedetto, R. L., \textit{heights and preperiodic points of polynomials over function fields}, Int. Math. Res. Not. IMRN, 62, 3855-3866, (2005) Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Heights, Other nonalgebraically closed ground fields in algebraic geometry Heights and preperiodic points of polynomials over function fields,
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(\ell \)-adic étale cohomology; Gauss sums; Hodge index theorem; Tate- Birch-Swinnerton-Dyer conjecture; crystalline cohomology Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Cycles and subschemes, Algebraic functions and function fields in algebraic geometry, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Étale and other Grothendieck topologies and (co)homologies, Arithmetic theory of algebraic function fields, \(p\)-adic cohomology, crystalline cohomology Gauss sums and algebraic cycles
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) applications to generalized Lüroth problem; Samuel problem; Zariski; problem; unirationality; ruled fields Transcendental field extensions, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On ruled 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 \(x^n+y^m+1=0\) Manin Yu.I.: The Hasse--Witt matrix of an algebraic curve. Trans. Amer. Math. Soc. 45, 245--246 (1965) Cyclotomic function fields (class groups, Bernoulli objects, etc.), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry The Hasse-Witt matrix of an algebraic curve
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) A.J. van der Poorten, Curves of genus \( 2\), continued fractions and Somos Sequences, J. Integer Seq. 8 (2005), Article 05.3.4. Continued fractions, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Algebraic functions and function fields in algebraic geometry Curves of genus 2, 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 \(x^n+y^m+1=0\) excellent function field; curve of genus 0; quadratic forms over function fields M. Rost, On quadratic forms isotropic over the function field of a conic, Mathematische Annalen 288 (1990), 511--513. Arithmetic theory of algebraic function fields, Quadratic forms over global rings and fields, Algebraic functions and function fields in algebraic geometry On quadratic forms isotropic over the function field of a conic
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 gap; function field; hyperelliptic curve Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences, Arithmetic theory of algebraic function fields On a construction of algebraic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois cohomology; theorem of Tate and Poitou; duality; one variable function field; quasi-finite field Douai, J. C.: Le théorème de Tate-poitou pour LES corps de fonctions des courbes. Comm. algebra 15, No. 11, 2379-2390 (1987) Galois cohomology, Algebraic functions and function fields in algebraic geometry, Power series rings, Arithmetic theory of algebraic function fields, Class field theory Le théorème de Tate-Poitou pour les corps de fonctions des courbes définies sur les corps de séries formelles en une variable sur un corps algébriquement clos. (The Tate-Poitou theorem for the function fields of curves defined on the fields of formal series in one variable over an algebraically closed 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 \(x^n+y^m+1=0\) hyperelliptic curve; discriminant; Szpiro conjecture Nguyen, K. V.: Non semistable Arakelov bound and hyperelliptic Szpiro ratio for function field, Proc. amer. Math. soc. 127, No. 11, 3125-3130 (1999) Algebraic functions and function fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Curves of arbitrary genus or genus \(\ne 1\) over global fields Non-semistable Arakelov bound and hyperelliptic Szpiro ratio for function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) additive combinatorics; function fields Arithmetic theory of algebraic function fields, Additive number theory; partitions, Combinatorial aspects of commutative algebra, Algebraic functions and function fields in algebraic geometry Towards a function field version of Freiman'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 \(x^n+y^m+1=0\) representation of group as automorphism group of algebraic function field; genus; inequality of Castelnuovo-Severi Joseph G. D'Mello and Manohar L. Madan, Algebraic function fields with solvable automorphism group in characteristic \?, Comm. Algebra 11 (1983), no. 11, 1187 -- 1236. Transcendental field extensions, Arithmetic theory of algebraic function fields, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory Algebraic function fields with solvable automorphism group 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 \(x^n+y^m+1=0\) Riemann hypothesis over finite fields; Weil conjectures Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, History of number theory, History of algebraic geometry, Curves over finite and local fields The Riemann hypothesis over finite fields: from Weil to the present day
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Brauer groups; indices; exponents; purely transcendental extensions; finitely generated extensions; function fields; projective spaces; projective curves Finite-dimensional division rings, Brauer groups (algebraic aspects), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Indices of central simple algebras over function fields of projective spaces over \(P_{n,r}\)-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 \(x^n+y^m+1=0\) units; function fields; number fields; affine étale curve Units and factorization, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Units in number fields and in function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) History of algebraic geometry, Biographies, obituaries, personalia, bibliographies, Algebraic functions and function fields in algebraic geometry, History of mathematics in the 19th century, Arithmetic theory of algebraic function fields, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials The theory of algebraic functions of one variable. Translated from the German, introduced and annotated by Emmylou Haffner
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) field of algebraic functions; \(GE_ 2\)-ring Abramenko, P.: Über einige diskret normierte functionenringe, die keine GE2-ringe sind. Arch. math. 46, 233-239 (1986) Arithmetic theory of algebraic function fields, Endomorphism rings; matrix rings, \(K\)-theory of global fields, Algebraic functions and function fields in algebraic geometry, Linear algebraic groups over global fields and their integers, Generators, relations, and presentations of groups, Subgroup theorems; subgroup growth On some discretely normed rings of functions being not \(GE_ 2\)-rings.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) fields of algebraic functions; matrix Riemann boundary problem; Riemann surface Algebraic functions and function fields in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences, Arithmetic theory of algebraic function fields On the construction of normal bases of rings of integral elements of some fields of algebraic functions
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves over finite fields; large numbers of rational points; Drinfeld modules; abelian reciprocity laws Drinfel'd modules; higher-dimensional motives, etc., Curves over finite and local fields, Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Algebraic coding theory; cryptography (number-theoretic aspects), Geometric methods (including applications of algebraic geometry) applied to coding theory, Cyclotomic function fields (class groups, Bernoulli objects, etc.) Drinfeld modules of rank 1 and algebraic curves 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 \(x^n+y^m+1=0\) function field; projective curve; obstruction to the Hasse principle; conic bundles; rational point Antoine Ducros, L'obstruction de réciprocité à l'existence de points rationnels pour certaines variétés sur le corps des fonctions d'une courbe réelle, J. Reine Angew. Math. 504 (1998), 73 -- 114 (French, with English summary). Rational points, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Real algebraic and real-analytic geometry The reciprocity obstruction to the existence of rational points for certain varieties on 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 \(x^n+y^m+1=0\) stable fields; function fields; transcendence base K. Neumann, Every finitely generated regular field extension has a stable transcendence base. \textit{Israel J. Math}. \textbf{104} (1998), 221-260. MR1622303 Zbl 0923.12006 Transcendental field extensions, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory Every finitely generated regular field extension has a stable transcendence base
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; towers; cubic bivariate polynomial; Kummer towers; ramification locus; asymptotic behavior Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry On cubic Kummer type towers 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 \(x^n+y^m+1=0\) Hermitian function field; Chebyshev polynomial; finite field Garcia A., Stichtenoth H.: On Chebyshev polynomials and maximal curves. Acta Arith. 90, 301--311 (1999) Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On Chebyshev polynomials and maximal curves
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; finite fields; towers of function fields; Artin-Schreier extensions of function fields Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Thue-Mahler equations, Finite ground fields in algebraic geometry A class of Artin-Schreier towers with finite genus
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) exponential sums; Weil's Riemann hypothesis; zeta functions; curves; function fields in one variable Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Curves, function fields and the Riemann hypothesis
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field; tower; rational place; Riemann Hypothesis Garcia, Arnaldo; Stichtenoth, Henning; Rück, Hans-Georg, On tame towers over finite fields, J. Reine Angew. Math., 0075-4102, 557, 53-80, (2003) Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields On tame towers over finite fields.
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic function fields; arithmetic theory of correspondences Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Arithmetische Theorie der Korrespondenzen algebraischer Funktionenkörper. 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 \(x^n+y^m+1=0\) Bauer M., ''The Arithmetic of Certain Cubic Function Fields.'' Arithmetic theory of algebraic function fields, Cryptography, Algebraic functions and function fields in algebraic geometry, Algebraic number theory computations The arithmetic of certain cubic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) global function fields; rational places; curves over finite fields; asymptotic measure of \(\mathbb{F}_q\)-rational points; class field towers; codes; Gilbert-Varshamov bound Niederreiter, H.; Xing, C., Towers of global function fields with asymptotically many rational places and an improvement on the Gilbert-varshamov bound, Math. Nachr., 195, 171-186, (1998) Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects), Finite ground fields in algebraic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Bounds on codes Towers of global function fields with asymptotically many rational places and an improvement on the Gilbert-Varshamov bound
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) fundamental units; hyperelliptic fields; local-global principle; Jacobian varieties; hyperelliptic curves; torsion problem in Jacobians; fast algorithms; continued fractions Платонов, В. П., УМН, 69, 1-415, 3-38, (2014) Units and factorization, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic theory of algebraic function fields, Jacobians, Prym varieties Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational 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 \(x^n+y^m+1=0\) Bernoulli numbers; function field of one variable; Von Staudt-Clausen type decomposition theorem Chip Snyder, A concept of Bernoulli numbers in algebraic function fields, J. Reine Angew. Math. 307/308 (1979), 295 -- 308. Arithmetic theory of algebraic function fields, Bernoulli and Euler numbers and polynomials, Algebraic numbers; rings of algebraic integers, Algebraic functions and function fields in algebraic geometry, Elliptic curves A concept of Bernoulli numbers in algebraic function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) density of rational points; function field analogue of the generalized Mordell conjecture K. MAEHARA, On the higher dimensional Mordell conjecture over function fields, Osaka J. Math. 2 (1991), 255-261. Rational points, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields On the higher dimensional Mordell conjecture over function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function field; Ihara's constant; cubic tower N. Anbar, P. Beelen, N. Nguyen, The exact limit of some cubic towers, to appear in Contemporary Mathematics, proceedings of AGCT-15. Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields The exact limit of some cubic towers
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic functions of one variable Hensel, K., u.G. Landsberg: Theorie der algebraischen Funktionen einer Veränderlichen. Leipzig 1902. Algebraic functions and function fields in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Arithmetic theory of algebraic function fields, Research exposition (monographs, survey articles) pertaining to number theory Theorie der algebraischen Funktionen einer Variablen. Neudruck der 1. Aufl
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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 in one variable over real-closed ground fields; symmetries; automorphisms; Klein surfaces Algebraic functions and function fields in algebraic geometry, Real algebraic and real-analytic geometry, Arithmetic theory of algebraic function fields Algebraic function fields in one variable over real-closed ground 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 \(x^n+y^m+1=0\) Chebotarev's theorem; Galois covering; smooth projective curves; function field; number of unramified points; Frobenius conjugacy class Kumar Murty, Vijaya; Scherk, John, Effective versions of the Chebotarev density theorem for function fields, C. R. Acad. Sci. Paris Sér. I Math., 319, 6, 523-528, (1994) Arithmetic theory of algebraic function fields, Density theorems, Algebraic functions and function fields in algebraic geometry, Curves over finite and local fields Effective versions of the Chebotarev density theorem for function fields
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) characteristic p; Weierstrass points García, Arnaldo, On Weierstrass points on Artin-Schreier extensions of \(k(x)\), Math. Nachr., 144, 233-239, (1989), MR MR1037171 (91f:14021) Riemann surfaces; Weierstrass points; gap sequences, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields On Weierstrass points on Artin-Schreier extensions of k(x)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) function fields; Kummer extension; asymptotically good towers Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry New examples of asymptotically good Kummer type towers
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) differential extension field; function field of an abelian variety; extension of Fuchsian type; extension of Kolchin type Buium, A. : Corps différentiels et modules des variétés algébriques . C.R. Acad. Sci. Paris 299 (1984) 983-985. Algebraic functions and function fields in algebraic geometry, Algebraic moduli of abelian varieties, classification, Differential algebra, Arithmetic theory of algebraic function fields Corps différentiels et modules des variétés algébriques. (Differential fields and moduli of algebraic varieties)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) S. Lang, Galois Cohomology of Abelian Varieties over \(P\)-adic Fields , Notes based on letters from Tate, unpublished. Curves in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to number theory, Research exposition (monographs, survey articles) pertaining to field theory, Complex multiplication and moduli of abelian varieties, Analytic theory of abelian varieties; abelian integrals and differentials, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Complex multiplication and abelian varieties Elliptic functions. (Transl. from the English by S. A. Stepanov)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus 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; Ulm invariants; regular algebraic function field B. Fein, M. Schacher, and J. Sonn, Brauer groups of fields of genus zero, J. Algebra 114 (1988), no. 2, 479 -- 483. Arithmetic theory of algebraic function fields, Brauer groups of schemes, Abelian groups, Algebraic functions and function fields in algebraic geometry Brauer groups of fields of genus zero
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) preperiodic points; directed graphs; elliptic curves Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps, Families and moduli spaces in arithmetic and non-Archimedean dynamical systems, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Dynamical modular curves for quadratic polynomial maps
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Goss zeta function; Newton polygon; Riemann hypothesis Bautista-Ancona, V., Diaz-Vargas, J.: Index of maximality and Goss zeta function, preprint 2010 Zeta and \(L\)-functions in characteristic \(p\), Combinatorics of partially ordered sets, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Index of maximality and Goss zeta function
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Garcia-Stichtenoth tower; zeta function; Jacobian variety Mcguire, Gary; Zaytsev, Alexey: On the zeta functions of an optimal tower of function fields over F4, Contemp. math. 518, 327-338 (2010) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Arithmetic ground fields for curves On the zeta functions of an optimal tower of function fields over \(\mathbb{F}_4\)
| 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) tower of function fields; finite field; Artin-Schreier extension A. Garciaand H. Stichtenoth. Some Artin-Schreier towers are easy. Mosc.Math. J., 5 (2005), 767--774. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Thue-Mahler equations, Finite ground fields in algebraic geometry Some Artin-Schreier towers are easy
| 0 |
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