p-adic Gamma function and traces of Frobenius of elliptic curves

Rupam Barman; Neelam Saikia

paper

p-adic Gamma function and traces of Frobenius of elliptic curves

arXiv:1304.3321

Abstract

In \cite{mccarthy2}, McCarthy defined a function $_{n} G_{n} [\dots]$ using Teichmüller character of finite fields and quotients of $p$ -adic gamma function, and expressed the trace of Frobenius of elliptic curves in terms of special values of $_{2} G_{2} [\dots]$ . We establish two different expressions for the traces of Frobenius of elliptic curves in terms of the function $_{2} G_{2} [\dots]$ . As a result, we obtain two relations between special values of the function $_{2} G_{2} [\dots]$ with different parameters.

arXiv comment13 pages