HYPERGEOMETRIC FUNCTIONS OVER Fp AND RELATIONS TO ELLIPTIC CURVES AND MODULAR FORMS

被引：54

作者：

Fuselier, Jenny C. ^{[1
]}

机构：

[1] US Mil Acad, West Point, NY 10996 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2010年 / 138卷 / 01期

关键词：

VALUES;

D O I：

10.1090/S0002-9939-09-10068-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For primes p equivalent to 1 (mod 12), we present an explicit relation between the traces of Frobenius on a family of elliptic curves with j-invariant 1728/t and values of a particular F-2(1)-hypergeometric function over F-p. We also give a formula for traces of Hecke operators on spaces of cusp forms of weight k and level 1 in terms of the same traces of Frobenius. This leads to formulas for Ramanujan's tau-function in terms of hypergeometric functions.

引用

页码：109 / 123

页数：15

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