Global function fields with many rational places over the quinary field. II

• Autorzy: Harald Niederreiter , Chaoping Xing
• Języki publikacji: EN

Kategorie tematyczne

• 11G20: Curves over finite and local fields
• 14G15: Finite ground fields
• 11R58: Arithmetic theory of algebraic function fields
• 11G09: Drinfel\cprime d modules; higher-dimensional motives, etc.
• 14H05: Algebraic functions; function fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 86
• Numer: 3
• Strony: 277-288

Daty

wydano

1998

otrzymano

1998-06-22

Twórcy

autor

Harald Niederreiter

• Institut für Informationsverarbeitung, Österreichische Akademie der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria

autor

Chaoping Xing

• Department of Information Systems and Computer Science, The National University of Singapore, Lower Kent Ridge Road, Singapore 119260

Bibliografia

• [1] A. Garcia and H. Stichtenoth, Algebraic function fields over finite fields with many rational places, IEEE Trans. Inform. Theory 41 (1995), 1548-1563.
• [2] D. Goss, Basic Structures of Function Field Arithmetic, Springer, Berlin, 1996.
• [3] D. R. Hayes, Explicit class field theory for rational function fields, Trans. Amer. Math. Soc. 189 (1974), 77-91.
• [4] 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.
• [5] H. Niederreiter and C. P. Xing, Quasirandom points and global function fields, in: Finite Fields and Applications, S. Cohen and H. Niederreiter (eds.), Cambridge Univ. Press, Cambridge, 1996, 269-296.
• [6] 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.
• [7] H. Niederreiter and C. P. Xing, Drinfeld modules of rank 1 and algebraic curves with many rational points. II, Acta Arith. 81 (1997), 81-100.
• [8] H. Niederreiter and C. P. Xing, Global function fields with many rational places over the quinary field, Demonstratio Math. 30 (1997), 919-930.
• [9] H. Niederreiter and C. P. Xing, The algebraic-geometry approach to low-discrepancy sequences, in: Monte Carlo and Quasi-Monte Carlo Methods 1996, H. Niederreiter et al. (eds.), Lecture Notes in Statist. 127, Springer, New York, 1998, 139-160.
• [10] H. Niederreiter and C. P. Xing, Algebraic curves over finite fields with many rational points, in: Number Theory, K. Győry, A. Pethő, and V. T. Sós (eds.), de Gruyter, Berlin, 1998, 423-443.
• [11] H. Niederreiter and C. P. Xing, Global function fields with many rational places and their applications, in: Proc. Finite Fields Conf. (Waterloo, 1997), Contemp. Math., Amer. Math. Soc., Providence, to appear.
• [12] H. Niederreiter and C. P. Xing, Nets, (t,s)-sequences, and algebraic geometry, in: Pseudo- and Quasi- Random Point Sets, P. Hellekalek and G. Larcher (eds.), Lecture Notes in Statist., Springer, New York, to appear.
• [13] O. Pretzel, Codes and Algebraic Curves, Oxford Univ. Press, Oxford, 1998.
• [14] M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), 365-378.
• [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] H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993.
• [17] G. van der Geer and M. van der Vlugt, How to construct curves over finite fields with many points, in: Arithmetic Geometry, F. Catanese (ed.), Cambridge Univ. Press, Cambridge, 1997, 169-189.
• [18] 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.
• [19] C. P. Xing and H. Niederreiter, Drinfeld modules of rank 1 and algebraic curves with many rational points, Monatsh. Math., to appear.