PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1997 | 81 | 1 | 81-100
Tytuł artykułu

Drinfeld modules of rank 1 and algebraic curves with many rational points. II

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Twórcy
  • Institut für Informationsverarbeitung, Österreichische Akademie der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria
  • Department of Mathematics, University of Science and, Technology of China, Hefei, Anhui 230026, P.R. China
Bibliografia
  • [1] A. Garcia and H. Stichtenoth, A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound, Invent. Math. 121 (1995), 211-222.
  • [2] A. Garcia and H. Stichtenoth, Algebraic function fields over finite fields with many rational places, IEEE Trans. Inform. Theory 41 (1995), 1548-1563.
  • [3] A. Garcia and H. Stichtenoth, On the asymptotic behaviour of some towers of function fields over finite fields, J. Number Theory 61 (1996), 248-273.
  • [4] D. R. Hayes, Stickelberger elements in function fields, Compositio Math. 55 (1985), 209-239.
  • [5] D. R. Hayes, A brief introduction to Drinfeld modules, in: The Arithmetic of Function Fields, D. Goss, D. R. Hayes, and M. I. Rosen (eds.), de Gruyter, Berlin, 1992, 1-32.
  • [6] Y. Ihara, Some remarks on the number of rational points of algebraic curves over finite fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), 721-724.
  • [7] H. Niederreiter and C. P. Xing, Low-discrepancy sequences and global function fields with many rational places, Finite Fields Appl. 2 (1996), 241-273.
  • [8] H. Niederreiter and C. P. Xing, Quasirandom points and global function fields, in: Finite Fields and Applications, S. D. Cohen and H. Niederreiter (eds.), Cambridge University Press, Cambridge, 1996, 269-296.
  • [9] H. Niederreiter and C. P. Xing, Explicit global function fields over the binary field with many rational places, Acta Arith. 75 (1996), 383-396.
  • [10] H. Niederreiter and C. P. Xing, Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places, Acta Arith. 79 (1997), 59-76.
  • [11] M. Perret, Tours ramifiées infinies de corps de classes, J. Number Theory 38 (1991), 300-322.
  • [12] M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), 365-378.
  • [13] R. Schoof, Nonsingular plane cubic curves over finite fields, J. Combin. Theory Ser. A 46 (1987), 183-211.
  • [14] R. Schoof, Algebraic curves over 𝔽₂ with many rational points, J. Number Theory 41 (1992), 6-14.
  • [15] J.-P. Serre, Sur le nombre des points rationnels d'une courbe algébrique sur un corps fini, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 397-402.
  • [16] J.-P. Serre, Nombres de points des courbes algébriques sur $𝔽_q$, in: Sém. Théorie des Nombres 1982-1983, Exp. 22, Univ. de Bordeaux I, Talence, 1983.
  • [17] J.-P. Serre, Résumé des cours de 1983-1984, Annuaire du Collège de France (1984), 79-83.
  • [18] J.-P. Serre, Rational Points on Curves over Finite Fields, lecture notes, Harvard University, 1985.
  • [19] J.-P. Serre, Personal communication, September 1995.
  • [20] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986.
  • [21] H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993.
  • [22] M. A. Tsfasman and S. G. Vlǎdut, Algebraic-Geometric Codes, Kluwer, Dordrecht, 1991.
  • [23] G. van der Geer and M. van der Vlugt, Curves over finite fields of characteristic 2 with many rational points, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), 593-597.
  • [24] G. van der Geer and M. van der Vlugt, How to construct curves over finite fields with many rational points, in: Proc. Conf. Algebraic Geometry (Cortona, 1995), to appear.
  • [25] W. C. Waterhouse, Abelian varieties over finite fields, Ann. Sci. Ecole Norm. Sup. (4) 2 (1969), 521-560.
  • [26] C. P. Xing, Multiple Kummer extension and the number of prime divisors of degree one in function fields, J. Pure Appl. Algebra 84 (1993), 85-93.
  • [27] C. P. Xing and H. Niederreiter, A construction of low-discrepancy sequences using global function fields, Acta Arith. 73 (1995), 87-102.
  • [28] C. P. Xing and H. Niederreiter, Modules de Drinfeld et courbes algébriques ayant beaucoup de points rationnels, C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), 651-654.
  • [29] C. P. Xing and H. Niederreiter, Drinfeld modules of rank 1 and algebraic curves with many rational points, preprint, 1996.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav81i1p81bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.