Rational Points over Finite Fields on a Family of Higher Genus Curves and Hypergeometric Functions

被引：4

作者：

Sung, Yih ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math, Van Vleck Hall,480 Lincoln Dr, Madison, WI 53706 USA

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2017年 / 21卷 / 01期

关键词：

Riemann surfaces; Rational points; Holomorphic differentials; Hypergeometric functions;

D O I：

10.11650/tjm.21.2017.7724

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we investigate the relation between the number of rational points over a finite field F-p(n). on a family of higher genus curves and their periods in terms of hypergeometric functions. For the case y(l) = x(x - 1)(x - lambda) we find a closed form in terms of hypergeometric functions associated with the periods of the curve. For the general situation y(l) = x(1)(a) (x - 1)(a)(2) (x - lambda)(a)(3) we show that the number of rational points is a linear combination of hypergeometric series, and we provide an algorithm to determine the coefficients involved.

引用

页码：55 / 79

页数：25