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1997 | 79 | 1 | 59-76
Tytuł artykułu

Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
79
Numer
1
Strony
59-76
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-04-19
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] L. Carlitz, A class of polynomials, Trans. Amer. Math. Soc. 43 (1938), 167-182.
  • [2] 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.
  • [3] A. Garcia and H. Stichtenoth, On the asymptotic behaviour of some towers of function fields over finite fields, J. Number Theory, to appear.
  • [4] D. R. Hayes, Explicit class field theory for rational function fields, Trans. Amer. Math. Soc. 189 (1974), 77-91.
  • [5] D. R. Hayes, Stickelberger elements in function fields, Compositio Math. 55 (1985), 209-239.
  • [6] 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.
  • [7] 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.
  • [8] R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, revised ed., Cambridge University Press, Cambridge, 1994.
  • [9] H. Niederreiter and C. P. Xing, Low-discrepancy sequences and global function fields with many rational places, Finite Fields Appl. 2 (1996), 241-273.
  • [10] H. Niederreiter and C. P. Xing, Explicit global function fields over the binary field with many rational places, Acta Arith. 75 (1996), 383-396.
  • [11] 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.
  • [12] M. Perret, Tours ramifiées infinies de corps de classes, J. Number Theory 38 (1991), 300-322.
  • [13] H.-G. Quebbemann, Cyclotomic Goppa codes, IEEE Trans. Inform. Theory 34 (1988), 1317-1320.
  • [14] M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), 365-378.
  • [15] R. Schoof, Algebraic curves over 𝔽₂ with many rational points, J. Number Theory 41 (1992), 6-14.
  • [16] 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.
  • [17] J.-P. Serre, Nombres de points des courbes algébriques sur $𝔽_q$, Sém. Théorie des Nombres 1982-1983, Exp. 22, Univ. de Bordeaux I, Talence, 1983.
  • [18] J.-P. Serre, Résumé des cours de 1983-1984, Annuaire du Collège de France (1984), 79-83.
  • [19] J.-P. Serre, Rational Points on Curves over Finite Fields, lecture notes, Harvard University, 1985.
  • [20] H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993.
  • [21] M. A. Tsfasman and S. G. Vlădut, Algebraic-Geometric Codes, Kluwer, Dordrecht, 1991.
  • [22] 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.
  • [23] G. van der Geer and M. van der Vlugt, How to construct curves over finite fields with many rational points, preprint, 1995.
  • [24] C. Voß and T. Høholdt, A family of Kummer extensions of the Hermitian function field, Comm. Algebra 23 (1995), 1551-1566.
  • [25] 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.
  • [26] C. P. Xing and H. Niederreiter, A construction of low-discrepancy sequences using global function fields, Acta Arith. 73 (1995), 87-102.
  • [27] 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.
  • [28] C. P. Xing and H. Niederreiter, Drinfeld modules of rank 1 and algebraic curves with many rational points, preprint, 1996.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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