PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2000 | 95 | 2 | 97-122
Tytuł artykułu

Ray class fields of global function fields with many rational places

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Twórcy
autor
  • Afd. wiskunde, Rijksuniversiteit Groningen, Blauwborgje 3 NL-9747 AC Groningen, The Netherlands
Bibliografia
  • [1] R. Auer, Ray class fields of global function fields with many rational places, Dissertation at the University of Oldenburg, www.bis.uni-oldenburg.de/dissertation/ediss.html, 1999.
  • [2] J. W. S. Cassels and A. Fröhlich, Algebraic Number Theory, Academic Press, New York, 1967.
  • [3] H. Cohen, F. Diaz y Diaz and M. Olivier, Computing ray class groups, conductors and discriminants, in: Algorithmic Number Theory, H. Cohen (ed.), Lecture Notes in Comput. Sci. 1122, Springer, 1996, 49-57.
  • [4] K M. Daberkow, C. Fieker, J. Klüners, M. Pohst, K. Roegner, M. Schörnig and K. Wildanger, KANT V4, J. Symbolic Comput. 24 (1997), 267-283.
  • [5] R. Fuhrmann and F. Torres, The genus of curves over finite fields with many rational points, Manuscripta Math. 89 (1996), 103-106.
  • [6] A. Garcia and H. Stichtenoth, Algebraic function fields over finite fields with many rational places, IEEE Trans. Inform. Theory 41 (1995), 1548-1563.
  • [7] G. van der Geer and M. van der Vlugt, How to construct curves over finite fields with many points, in: Arithmetic Geometry (Cortona, 1984), F. Catanese (ed.), Cambridge Univ. Press, 1997, 169-189.
  • [8] G. van der Geer and M. van der Vlugt, Constructing curves over finite fields with many points by solving linear equations, preprint, 1997.
  • [9] G. van der Geer and M. van der Vlugt, Tables of curves with many points, preprint at http://www.wins.uva.nl/geer, 1999.
  • [10] H H. Hasse, Number Theory, Springer, Berlin, 1980.
  • [11] D. R. Hayes, Explicit class field theory in global function fields, in: Studies in Algebra and Number Theory, Adv. in Math. Suppl. Stud. 6, Academic Press, 1979, 173-217.
  • [12] H. Kisilevsky, Multiplicative independence in function fields, J. Number Theory 44 (1993), 352-355.
  • [13] K. Lauter, Ray class field constructions of curves over finite fields with many rational points, in: Algorithmic Number Theory, H. Cohen (ed.), Lecture Notes in Comput. Sci. 1122, Springer, 1996, 187-195.
  • [14] K. Lauter, Deligne-Lusztig curves as ray class fields, Manuscripta Math. 98 (1999), 87-96.
  • [15] K. Lauter, A formula for constructing curves over finite fields with many rational points, J. Number Theory 74 (1999), 56-72.
  • [16] J. Neukirch, Algebraische Zahlentheorie, Springer, Berlin, 1991.
  • [17] H. Niederreiter, Nets, (t,s)-sequences, and algebraic curves over finite fields with many rational points, in: Proc. Internat. Congress of Math. (Berlin, 1998), Documenta Math. Extra Vol. ICM III (1998), 377-386.
  • [18] H. Niederreiter and C. P. Xing, Explicit global function fields over the binary field with many rational places, Acta Arith. 75 (1996), 383-396.
  • [19] H. Niederreiter and C. P. Xing, Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places, ibid. 79 (1997), 59-76.
  • [20] H. Niederreiter and C. P. Xing, Drinfeld modules of rank 1 and algebraic curves with many rational points. II, ibid. 81 (1997), 81-100.
  • [21] H. Niederreiter and C. P. Xing, Algebraic curves over finite fields with many rational points, in: Proc. Number Theory Conf. (Eger, 1996), de Gruyter, 1998, 423-443.
  • [22] H. Niederreiter and C. P. Xing, Global function fields with many rational places over the ternary field, Acta Arith. 83 (1998), 65-86.
  • [23] H. Niederreiter and C. P. Xing, Global function fields with many rational places over the quinary field, Demonstratio Math. 30 (1997), 919-930.
  • [24] H. Niederreiter and C. P. Xing, Global function fields with many rational places over the quinary field. II, Acta Arith. 86 (1998), 277-288.
  • [25] H. Niederreiter and C. P. Xing, Algebraic curves with many rational points over finite fields of characteristic 2, in: Number Theory in Progress (Zakopane, 1997), Vol. 1, de Gruyter, 1999, 359-380.
  • [26] H. Niederreiter and C. P. Xing, A general method of constructing global function fields with many rational places, in: Algorithmic Number Theory (Portland, 1998), Lecture Notes in Comput. Sci. 1423, Springer, 1998, 555-566.
  • [27] H. Niederreiter and C. P. Xing, Algebraic curves over finite fields with many rational points and their applications, in: Number Theory, V. C. Dumir et al. (eds.), Indian National Science Academy, to appear.
  • [28] H. Niederreiter and C. P. Xing, Global function fields with many rational places and their applications, Contemp. Math. 225 (1999), 87-111.
  • [29] J. P. Pedersen, A function field related to the Ree group, in: Coding Theory and Algebraic Geometry (Luminy, 1991), H. Stichtenoth and M. A. Tsfasman (eds.), Lecture Notes in Math. 1518, Springer, Berlin, 1992, 122-131.
  • [30] M. Perret, Tours ramifiées infinies de corps de classes, J. Number Theory 38 (1991), 300-322.
  • [31] M. Rosen, S-units and S-class group in algebraic function fields, J. Algebra 26 (1973), 98-108.
  • [32] M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), 365-378.
  • [33] R. Schoof, Algebraic Curves and Coding Theory, UTM 336 (1990), Univ. of Trento.
  • [34] J.-P. Serre, Sur le nombre des points rationnelles d'une courbe algébrique sur un corps fini, C. R. Acad. Sci. Paris Sér. I 296 (1983), 397-402.
  • [35] J.-P. Serre, Nombres de points des courbes algébrique sur $𝔽_q$, Sém. Théor. Nombres Bordeaux 22 (1982//83).
  • [36] J.-P. Serre, Résumé des cours de 1983-1984, Annuaire du Collège de France, 1984, 79-83.
  • [37] H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993.
  • [38] C. P. Xing and H. Niederreiter, Drinfel'd modules of rank 1 and algebraic curves with many rational points, Monatsh. Math. 127 (1999), 219-241.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav95z2p97bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.