p-Adic gamma function and the trace of Frobenius of elliptic curves

JOURNAL OF NUMBER THEORY

卷:140

Article

Barman, Rupam¹  Saikia, Lam¹ 

[1] Indian Inst Technol, Dept Math, New Delhi 110016, India

关键词: Trace of Frobenius;    Elliptic curves;    Characters of finite fields;    Gauss sums;    Teichmuller character;    p-Adic gamma function;   

DOI  :  10.1016/j.jnt.2014.01.026

来源: Elsevier

【 摘 要 】

In [12], McCarthy defined a function (n)G(n)[...] using the Teichmuller character of finite fields and quotients of the p-adic gamma function, and expressed the trace of Frobenius of elliptic curves in terms of special values of (2)G(2)[...]. We establish two different expressions for the traces of Frobenius of elliptic curves in terms of the function (2)G(2)[...]. As a result, we obtain two transformation formulas of the function (2)G(2)[...] with different parameters. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free