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

被引：56
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.
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页码：109 / 123
页数：15
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