Drinfeld modules of rank 1 and algebraic curves with many rational points. II
Harald Niederreiter; Chaoping Xing
Acta Arithmetica (1997)
- Volume: 81, Issue: 1, page 81-100
- ISSN: 0065-1036
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topHarald Niederreiter, and Chaoping Xing. "Drinfeld modules of rank 1 and algebraic curves with many rational points. II." Acta Arithmetica 81.1 (1997): 81-100. <http://eudml.org/doc/207057>.
@article{HaraldNiederreiter1997,
author = {Harald Niederreiter, Chaoping Xing},
journal = {Acta Arithmetica},
keywords = {Drinfeld modules of rank 1; algebraic curves; many rational points; finite field},
language = {eng},
number = {1},
pages = {81-100},
title = {Drinfeld modules of rank 1 and algebraic curves with many rational points. II},
url = {http://eudml.org/doc/207057},
volume = {81},
year = {1997},
}
TY - JOUR
AU - Harald Niederreiter
AU - Chaoping Xing
TI - Drinfeld modules of rank 1 and algebraic curves with many rational points. II
JO - Acta Arithmetica
PY - 1997
VL - 81
IS - 1
SP - 81
EP - 100
LA - eng
KW - Drinfeld modules of rank 1; algebraic curves; many rational points; finite field
UR - http://eudml.org/doc/207057
ER -
References
top- [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. Zbl0822.11078
- [2] A. Garcia and H. Stichtenoth, Algebraic function fields over finite fields with many rational places, IEEE Trans. Inform. Theory 41 (1995), 1548-1563. Zbl0863.11040
- [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. Zbl0893.11047
- [4] D. R. Hayes, Stickelberger elements in function fields, Compositio Math. 55 (1985), 209-239. Zbl0569.12008
- [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. Zbl0793.11015
- [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. Zbl0509.14019
- [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. Zbl0932.11050
- [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. Zbl0877.11065
- [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. Zbl0891.11057
- [11] M. Perret, Tours ramifiées infinies de corps de classes, J. Number Theory 38 (1991), 300-322. Zbl0741.11044
- [12] M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), 365-378. Zbl0632.12017
- [13] R. Schoof, Nonsingular plane cubic curves over finite fields, J. Combin. Theory Ser. A 46 (1987), 183-211. Zbl0632.14021
- [14] R. Schoof, Algebraic curves over 𝔽₂ with many rational points, J. Number Theory 41 (1992), 6-14. Zbl0762.11026
- [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. Zbl0538.14015
- [16] J.-P. Serre, Nombres de points des courbes algébriques sur , 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. Zbl0585.14026
- [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. Zbl0727.94007
- [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. Zbl0787.14033
- [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. Zbl0884.11027
- [25] W. C. Waterhouse, Abelian varieties over finite fields, Ann. Sci. Ecole Norm. Sup. (4) 2 (1969), 521-560. Zbl0188.53001
- [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. Zbl0776.11068
- [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. Zbl0853.11051
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