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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) function fields; curves of genus greater than 1; finite number of points defined over the ground 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) groups; linear algebra; infinite dimensional spaces; systems of linear differential equations; symmetry; finite subgroups of rotation group; free groups; generators; relations; Todd-Coxeter algorithm; bilinear forms; spectral theorems; linear groups; group representations; rings; algebraic geometry; factorization; modules; function fields and their relations to Riemann surfaces; Galois theory | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Bogomolov conjecture; curves of higher genus; function fields; metric graphs Faber, X. W. C., The geometric Bogomolov conjecture for curves of small genus, Experiment. Math., 1058-6458, 18, 3, 347\textendash 367 pp., (2009) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) finiteness of group of automorphisms; one-dimensional connected affine 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 properties of hyperelliptic function fields; minimum distance of geometric codes; hyperelliptic curves Xing, C. -P.: Hyperelliptic function fields and codes. J. pure appl. Algebra 74, 109-118 (1991) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) algebraic function fields; algebraic curves; distributions of values DOI: 10.1090/S0002-9947-06-04018-9 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) indecomposable division algebras; noncrossed product division algebras; patching over fields; smooth projective curves; completions of function fields; Brauer groups Chen, F.: Indecomposable and noncrossed product division algebras over curves over complete discrete valuation rings, (2010) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) characteristic \(p\); Galois group of number fields of curves; elliptic curve; potentially good reduction Kraus, A., Sur le défaut de semi-stabilité des courbes elliptiques à réduction additive, Manuscripta Math., 69, 1, 353-385, (1990) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Ulm invariants; Brauer group of algebraic function fields over global fields Fein, B.; Schacher, M.: Brauer groups of algebraic function fields. J. algebra 103, 454-465 (1986) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) towers of function fields; rational places; genus of a function field; automorphisms of function fields; \(p\)-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) Riemann surfaces; algebraic curves; automorphisms; fields of moduli Hidalgo, R. A., Erratum: non-hyperelliptic Riemann surfaces with real field of moduli but not definable over the reals, Arch. Math., 98, pp., (2012) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) reduced Whitehead groups; Tannaka-Artin problem; patching; \(\mathrm{SK}_1\); function fields of \(p\)-adic curves | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) classification of real affine cubic curves; group of homeomorphisms D.A. Weinberg, The topological classification of cubic curves , Rocky Mountain J. Math. 18 (1988), 665-679. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) function fields of \(p\)-adic curves; classical groups; projective homogeneous spaces; local-global principle; 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) Birch--Swinnerton-Dyer conjecture; rank; group of rational points; elliptic curves; class number; quadratic 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) elliptic curves over function fields; Mordell-Weil rank; Néron-Tate regulator; Tate-Shafarevich group; \(L\)-function; BSD 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) isotriviality; effective Mordell; semiabelian variety; positive characteristic; survey of diophantine geometry; bounding the heights of rational points on curves over function fields; semiabelian varieties; Roth's theorem Voloch, José Felipe, Diophantine geometry in characteristic \(p\): a survey.Arithmetic geometry, Cortona, 1994, Sympos. Math., XXXVII, 260-278, (1997), Cambridge Univ. Press, Cambridge | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) false division towers; modular function fields; principal congruence subgroup; Galois group; elliptic curves Rohrlich, D. E.: False division towers of elliptic curves. J. algebra (2000) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) affine variety; group of automorphisms; fixed point of a polynomial automorphism | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) De Rham cohomology; crystalline action of Weil group; Morita's \(p\)-adic gamma function; absolute Hodge cycles; Frobenius matrix of Fermat curves Ogus, A, A \(p\)-adic analogue of the chowla-Selberg formula, \(p\)-adic analysis (Trento, 1989), Lect. Notes Math., 1454, 319-341, (1990) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) class numbers; Tamagawa numbers; Tate-Shafarevich sets; pseudo-reductive groups; affine group schemes; global function fields Gille, P.: Torseurs sur la droite affine et R-équivalence. Thèse Dr. Sci., Univ. Paris-Sud (1997). See also Gille, P.: Torseurs sur la droite affine. Trans. Gr. \textbf{7}, 231-245 (2002) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) zeta function of a number field; arithmetically equivalent number fields; Gassmann triple; permutation representations; integral representations; idele class groups; algebraic curves; 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) Frobenius endomorphisms; curves over finite fields; projective curve of genus 5; zeta function Lauter K., Proceedings of the American Mathematical Society 128 (2) pp 369-- (2000) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) theory of algebraic curves; coding theory; Riemann-Roch theorem; function fields; differentials; Hasse-Weil theorem; geometric Goppa codes; trace codes H. Stichtenoth, Algebraic Function Fields and Codes, Second edn, (Springer-Verlag, Berlin Heidelberg, 2009). Zbl0816.14011 MR2464941 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) automorphisms of algebraic curves; order of the automorphism group A. Seyama , A characterization of reducible abelian varieties , to appear. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) cuspidal class number formula; modular curves; divisors; group of modular units; Dedekind eta-function; analog of Stickelberger ideal T. Takagi, The cuspidal class number formula for the modular curves \(X_0(M)\) with \(M\) square-free, J. Alg. 193 (1997), 180-213. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) elliptic curves; function fields; Tate-Shafarevich group Ulmer, Douglas: Explicit points on the Legendre curve III. (2014) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) class field theory for curves over local fields; abelian fundamental group; class field theory of two-dimensional local fields; reciprocity law Saito S.: Class field theory for curves over local fields. J. Number Theory 21(1), 44--80 (1985) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) elliptic curves over finite fields; distribution of group orders | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) automorphism groups of algebraic function fields; realization of group as Galois group; Galois theory Henning Stichtenoth, Zur Realisierbarkeit endlicher Gruppen als Automorphismengruppen algebraischer Funktionenkörper, Math. Z. 187 (1984), no. 2, 221 -- 225 (German). | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Galois theory; algebraic fundamental groups; finite simple group; wreath product; Galois group; unramified covering of the affine line; group enlargements; enlargements; tame fundamental groups of curves Abhyankar, S. S.: Group enlargements. CR acad. Sci. Paris 312, 763-768 (1991) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) alternative algebra; quadratic algebra; composition algebras; algebraic curves of genus zero; locally ringed spaces; Cayley-Dickson doubling process; Zorn's vector matrices; octonion algebras; Zorn algebras; function fields of genus zero; polynomial rings Petersson, H.: Composition algebras over algebraic curves of genus 0. Trans. Am. Math. Soc. 337, 473--491 (1993) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) elliptic curves over finite fields; discrete elliptic logarithm function; public key cryptosystems; twisted pair 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) Weierstraß \(\wp\)-function; Mordell's theorem; Hasse's theorem; \(L\)- function; Birch and Swinnerton-Dyer conjecture; \(j\)-invariant; rational points of elliptic curves; imaginary quadratic fields; Taniyama-Weil conjecture Henri Cohen, Elliptic curves, From number theory to physics (Les Houches, 1989) Springer, Berlin, 1992, pp. 212 -- 237. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Abelian group; affine varieties; automorphisms; shift-action; compact Lie group; ring of Laurent polynomials; ergodicity; expansiveness; finiteness; number of periodic points Schmidt K. 1990 Automorphisms of compact abelian groups and affine varieties \textit{Proc. London Math. Soc. (3)}61 480-496 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) diophantine equations; equations over finite fields; arithmetic theory of algebraic curves; nonstandard arithmetic; zeta function; integral points on curves S. A. Stepanov, \textit{Arithmetic of Algebraic Curves} (Nauka, Moscow, 1991) [in Russian]. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) cartography; plane trees; Belyi functions; unicellular dessin; function fields of algebraic curves N. Adrianov and G. Shabat, ''Unicellular cartography and Galois orbits of plane trees,'' in: \textit{Geometric Galois Actions}, 2, (1997), pp. 13-24. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) lattices and their invariants; associated tori; elliptic functions; modular forms of one variable; periodic meromorphic functions; field of elliptic functions; Weierstrass \(\wp\)-function; elliptic curves; product representations; complex multiplication; Jacobi's theta series; Jacobi forms; modular functions; Siegel modular group; discontinuous subgroups; weight formula; Dedekind's eta-function; cusp forms; algebra of Hecke operators; Petersson inner product; Eisenstein series; Dirichlet series; functional equation; Hecke operators; harmonic polynomials; quadratic forms; Epstein zeta-function; Kronecker's limit formula; Rankin convolution M. Koecher and A. Krieg, \textit{Elliptische Funktionen und Modulformen}, Springer, Berlin, Heidelberg, 1998. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) differential operators; commutative affine \({\mathbb{C}}\)-algebra; coordinate ring; nonsingular affine variety; simple noetherian domain; Gelfand- Kirillov dimension; ring of invariants; group of automorphisms; simple noetherian ring; variety of symmetric n\(\times n\) matrices; simple factor ring; enveloping algebras; semisimple Lie algebras Levasseur, T.; Stafford, J. T., Rings of differential operators on classical rings of invariants, Mem. Amer. Math. Soc., 412, pp., (1989) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) simple Lie algebras; Lie algebras of algebraic; symplectic and Hamiltonian vector fields; smooth affine curves; Danielewski surfaces; locally nilpotent derivations | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) tower of function fields; genus; rational places; curves with many points A. Garcia, H. Stichtenoth, On the Galois closure of towers, preprint, 2005 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Riemann surfaces; Abelian integrals; algebraic number theory; function fields; valuations; function fields of curves; Abel-Jacobi theorem Cohn, P. M.: Algebraic numbers and algebraic functions, Chapman \& Hall math. Ser. (1991) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) group of automorphisms of smooth curve; \(L\)-functions; zeta-functions; Galois covering; class numbers; varieties over finite fields; Betti numbers; rank of the Mordell-Weil group; conjectures of Birch-Swinnerton-Dyer; Tate conjectures on algebraic cycles Kani, No article title, J. Number Theory, 46, 230, (1994) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) first order theory of function fields in the language of fields; curves; undecidability Jean-Louis Duret, Sur la théorie élémentaire des corps de fonctions, J. Symbolic Logic 51 (1986), no. 4, 948 -- 956. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Witt rings of function fields; real analytic manifold; second residue class homomorphism; Artin-Lang property; Witt group of the ring of real analytic 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) Semi-stable and stable vector bundles on regular projective curves; moduli space of stable bundles; local non-abelian zeta functions for curves defined over finite fields (rationality and functional equations); global non-abelian zeta functions for curves defined over number fields; non-abelian L--functions for function fields (rationality and functional equations) Weng, L.: Non-abelian L function for 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) elliptic curve over the rational function field; ring of invariants; excellent families of elliptic curves; Weyl group; Mordell-Weil lattice of a rational elliptic surface Shioda, T; Usui, H, Fundamental invariants of Weyl groups and excellent families of elliptic curves, Comment. Math. Univ. St. Pauli, 41, 169-217, (1992) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) del Pezzo surfaces; fibrations; function fields of curves; rational points; intermediate Jacobians Hassett, B; Tschinkel, Y, Quartic del Pezzo surfaces over function fields of curves, Cent. Eur. J. Math., 12, 395-420, (2014) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Painlevé equations; Differential algebraic function fields; analytic subgroups; algebraic subgroups; birational automorphism group of a complex algebraic variety; Pfaffian differential equations over complex manifolds; algebraic differential equations N. N. Parfentiev, ''A review on the work by Prof. Schlesinger from Giessen,'' \textit{Izvestiya Fiz.-Mat. Obshchestva pri Imperat. Kazan. Universitete}, Ser. 2, \textbf{XVIII}, 4 (1912). | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) algebraic function field; group of automorphisms; finiteness; Weierstrass points Schmid, Über die Automorphismen eines algebraischen Funktionenkörpers von Primzahlcharakteriatik., J. reine angew. Math. 179 pp 5-- (1938) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) efficiency of function field sieve; discrete logarithms in finite fields; supersingular elliptic curves Granger, R., Holt, A., Page, D., Smart, N.P., Vercauteren, F.: Function field sieve in Characteristic three.In: Algorithmic Number Theory Symposium - ANTS VI, pp. 223--234. Springer LNCS 3076 (2004) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) explicit formulae of prime number theory; Riemann zeta-function; Poisson summation formula; Riemann hypothesis; Hadamard product formula; zeros; prime number theorem; Lindelöf hypothesis; zeta-functions attached to curves over finite fields; approximate functional equation; large number of exercises Patterson, S.J. (1988). An Introduction to the Theory of the Riemann Zeta-Function. Cambridge Studies in Advanced Mathematics 14 . Cambridge: Cambridge Univ. Press. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Teichmüller modular function fields; pro-\(l\) number field towers; moduli stack of smooth projective curves; stability; braid groups Nakamura, H.; Takao, N.; Ueno, R., Some stability properties of Teichmüller modular function fields with pro-\textit{} weight structures, Math. ann., 302, 197-213, (1995), MR 96h:14041 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) action of affine algebraic group; algebra automorphisms; minimal injective resolutions Magid, A, Cohomology of rings with algebraic group action, Adv. Math., 59, 124-151, (1986) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) function fields; irreducible polynomials; hyperelliptic curves; derivatives of \(L\)-functions; moments of \(L\)-functions; quadratic Dirichlet \(L\)-functions; random matrix theory | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) elliptic curves over function fields; explicit computation of \(L\)-functions; special values of \(L\)-functions and BSD conjecture; estimates of special values; analogue of the 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) singular cubics; isogenies; torsion points; elliptic curves over finite fields; elliptic curves over local fields; Selmer groups; duality; rational torsion; heights; complex multiplication; integral points; Galois representations; survey; group law; endomorphism ring; Weil pairing; elliptic functions; formal group; Shafarevich-Tate groups; \(L\)-series; Tate curves; descent; conjecture of Birch and Swinnerton-Dyer Silverman, J. H.: A survey of the arithmetic theory of elliptic curves. Modular forms and Fermat's last theorem (1997) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) quadratic forms; \(u\)-invariant; power series fields; function fields of curves; orderings of fields; patching of fields Scheiderer, Claus: The u-invariant of one-dimensional function fields over real power series fields, Arch. math. (Basel) 93, No. 3, 245-251 (2009) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) coverings of curves; projective curve; automorphism group; linear fractional transformation; algebraic function field; finite Galois extension; Galois 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) elliptic curves; number fields; torsion group; abelian 2-extensions of \(\mathbb{Q}\); \(K\)-isogeny class | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) algebraic function fields; finite field of constants; Severi's algebraic theory of correspondences; Hurwitz's transcendental theory; group of divisor classes; Riemann hypothesis for function fields; action of Galois group André Weil, Sur les fonctions algébriques à corps de constantes fini, C. R. Acad. Sci. Paris 210 (1940), 592 -- 594 (French). | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Brauer groups; indecomposable division algebras; noncrossed products; ramification; function fields of smooth curves; non-crossed product central division algebras; exponents; indices; periods; tensor products of central algebras E. Brussel, K. McKinnie, and E. Tengan, Indecomposable and noncrossed product division algebras over function fields of smooth \?-adic curves, Adv. Math. 226 (2011), no. 5, 4316 -- 4337. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Mordell-Weil group; multidimensional function fields; Néron-Tate height; Mordell-Weil rank; Jacobian; independence of some rational points T. Shioda, Constructing curves with high rank via symmetry, Amer. J. Math., to appear. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) effective geometric Bogomolov conjecture; curves of genus 3 over function fields; self-intersection of the relative dualizing sheaf; admissible constants of the metrized dual graph K. Yamaki, Geometric Bogomolov's conjecture for curves of genus 3 over function fields, J. Math. Kyoto Univ. 42 (2002), 57-81. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) division algebras; cyclic algebras; ramifications; étale cohomology; function fields of surfaces; affine schemes; Brauer groups; central algebras; fields of fractions; cyclic Galois extensions Colliot-Thélène, J.-L.: Conjectures de type local-global sur image des groupes de Chow dans la cohomologie étale. In: Algebraic K-theory (Seattle, WA, 1997), Proceedings of Symposia in Pure Mathematics, vol. 67, pp. 1-12. Amer. Math. Soc., Providence (1999) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) rational points; inseparable extensions of function field; Mordell conjecture for number fields; genus drop; prime characteristic; non-conservative curves Voloch, J. F.: A Diophantine problem on algebraic curves over function fields of positive characteristic. Bull. soc. Math. France 119, 121-126 (1991) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) genus \(\neq 1\); hyperelliptic involution; group of automorphisms of a curve; elliptic curves; isogenies; many rational points; algebraic curve; 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) p-adic L-functions; CM fields; totally complex quadratic extension of a totally real field; Grössencharacter; p-adic measure; p-adic interpolation of Hecke L-function; functional equation; non-analytic Eisenstein series; Hilbert modular group; p-adic differential operators; p-adic Eisenstein series N.M. Katz, ''p-Adic L-functions for CM-fields,'' Invent. Math. 49(3), 199--297 (1978). | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) motives; review of Iwasawa main conjecture; cyclotomic fields; elliptic curves; Selmer group; cyclotomic deformations of motives R. Greenberg, ''Iwasawa theory and \(p\)-adic deformations of motives,'' in Motives, II (Seattle, WA, 1991), Proc. Sympos. Pure Math. 55, Amer. Math. Soc., Providence, 1994, 193--223. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) thetanulls of cyclic curves; the group of automorphisms branch points of the projection; hyperelliptic curves Previato, E; Shaska, T; Wijesiri, GS, Thetanulls of cyclic curves of small genus, Albanian J. Math., 1, 253-270, (2007) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) \(L\)-series of number fields; infinite-dimensional analogue of one- parameter group; Artin formalism; self-adjoint operator; associated heat kernel; characteristic kernel; trace; asymptotic expansion; regularized determinant of the Laplacian; Selberg zeta function; theta functions J. Jorgenson, S. Lang, Artin formalism and heat kernels. Jour. Reine. Angew. Math. 447 (1994), 165-280. Zbl0789.11055 MR1263173 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) elliptic curves over function fields; Tate-Shafarevich groups; explicit computation of \(L\)-functions; BSD conjecture; Gauss and Kloosterman sums | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Iwasawa theory; supersingular reduction; Tate-Shafarevich group; p-adic L-function; Selmer groups; ring of norms; p-adic heights; supersingular elliptic curves Perrin-Riou, Bernadette, Theorie d'Iwasawa \textit{p}-adique locale et globale, Invent. Math., 99, 247-292, (1990) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) 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 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) 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 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Galois coverings of curves; group of automorphisms; genus of the quotient curve; Hasse-Witt invariants Kani, E. Relations between the genera and between the Hasse-Witt invariants of Galois coverings of curves. Canad. Math. Bull.28 (3), 321--327 (1985) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) representation theory of finite-dimensional algebras; tame hereditary algebras; tame bimodules; noncommutative curves of genus zero; noncommutative function fields of genus zero D. Kussin, Parameter curves for the regular representations of tame bimodules, J. Algebra, 320 (2008), no. 6, 2567--2582.Zbl 1197.16017 MR 2437515 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) finite fields; function fields; hyperelliptic curves; \(K\)-groups; moments of quadratic Dirichlet \(L\)-functions; class number Andrade, J. C.; Bae, S.; Jung, H., Average values of \textit{L}-series for real characters in function fields, Res. Math. Sci., 3, (2016), 47 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Galois representations; Mordell-Weil lattices; elliptic curves; deformation theory of isolated singularities; Mordell-Weil group; Hasse zeta function; elliptic surfaces; Artin L-function; Weil height; del Pezzo surfaces; cubic forms Shioda, T.: Mordell-Weil lattices and Galois representation. I, II, III. Proc. Japan Acad., 65A, 269-271 ; 296-299 ; 300-303 (1989). | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) finite fields; tame fundamental group; Markoff triples; tamely ramified covers; characteristic \(p\); covers 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) 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 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Artin-Schreier extensions of function fields; automorphisms; \(k\)-error linear complexity; joint linear complexity; multisequences | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) affine Cremona group; automorphism of the affine space; tame 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) explicit formulae of prime number theory; Riemann zeta-function; Poisson summation formula; Riemann hypothesis; Hadamard product formula; zeros; prime number theorem; Lindelöf hypothesis; zeta-functions attached to curves over finite fields; approximate functional equation; large number of exercises Patterson, S. J., An introduction to the theory of the Riemann zeta-function, (1995), Cambridge University Press | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) 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) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) linear algebraic groups; pseudo-reductive groups; generalized standard construction; groups locally of minimal type; structure and classification of pseudo-reductive groups; imperfect fields; pseudo-split groups; central extensions; affine group schemes Conrad, B.; Prasad, G., Classification of pseudo-reductive groups, Annals of Mathematics Studies, (2015), Princeton University Press | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Mordell-Weil theorem; rational points; \(p\)-descent; Selmer group; \(L\)- function; conjecture of Birch and Swinnerton-Dyer; Igusa curves Ulmer, D. L., P-descent in characteristic p, Duke Math. J., 62, 2, 237-265, (1991) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) 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 | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) curves defined over a valuation ring; function field; first order language of valued fields; stable reduction theorem [GMP] B. W. Green, M. Matignon and F. Pop,On valued function fields III, Reductions of algebraic curves, Journal für die Reine und Angewandte Mathematik432 (1992), 117--133. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) moduli space of smooth affine curves; curves with one place at infinity; genus; quotient space; automorphism group; rational variety Oka, M.: Moduli space of smooth affine curves of a given genus with one place at infinity. Prog. math. 162, 409-434 (1998) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) group of automorphisms; birational splitting theorem for the Albanese map; Albanese variety; meromorphic 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) linear algebraic group; R-equivalence; function fields of surfaces; weak approximation; Hasse principle Colliot-Thélène, J.-L.; Gille, P.; Parimala, R., Arithmetic of linear algebraic groups over two-dimensional geometric fields, Duke Math. J., 121, 285-341, (2004) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) curves of genus greater than one; computational aspects; number of points; Jacobian; finite fields; Mordell-Weil group; construction of curves Poonen, Bjorn, Computational aspects of curves of genus at least \(2\). Algorithmic number theory, Talence, 1996, Lecture Notes in Comput. Sci. 1122, 283-306, (1996), Springer, Berlin | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) 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) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Brauer group of function field; reciprocity sequence; higher-dimensional function fields; smooth projective varieties; threefolds J. -L. Colliot-Thélène, ''On the reciprocity sequence in the higher class field theory of function fields,'' in Algebraic \(K\)-Theory and Algebraic Topology, Dordrecht: Kluwer Acad. Publ., 1993, vol. 407, pp. 35-55. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) affine variety minus bound on the height of integral points; hyperplanes in general position; number of integral points; function fields Wang, J.T.-Y., \textit{S}-integral points of \(\mathbb{P}^n - \{2 n + 1 \text{ hyperplanes in general position} \}\) over number fields and function fields, Trans. amer. math. soc., 348, 3379-3389, (1996) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) classification of real affine cubic curves; action of the group of affine isomorphisms Weinberg D.A: affine classification of cubic curves. Rocky Mt. J. Math. 18(3), 655--664 (1988) | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) curves in characteristic p; p-adic Galois representations; group of automorphisms; Jacobian variety; Tate module R. Valentini,Some p-adic Galois representations for curves in characteristic p, Mathematische Zeitschrift192 (1986), 541--545. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) moduli space of curves; mapping class group; Riemann zeta function; Euler characteristic; configurations HZ J.~Harer and D.~Zagier, \emph The Euler characteristic of the moduli space of curves, Invent. Math. \textbf 85 (1986), no.~3, 457--485. | 0 |
group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) elliptic curves over finite fields; Weil conjectures; group of torsion; elliptic curves over local fields; good reduction; elliptic curves over global fields; Mordell-Weil theorem; descent; Selmer group; Shafarevich groups J. H. Silverman, \textit{The Arithmetic of Elliptic Curves.}Springer Verlag, New York, 1986. | 0 |
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