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arXiv · 1304.3321

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

Rupam Barman·Neelam Saikia
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Abstract

In \cite{mccarthy2}, McCarthy defined a function $_{n}G_{n}[\cdots]$ 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 $_{2}G_{2}[\cdots]$. We establish two different expressions for the traces of Frobenius of elliptic curves in terms of the function $_{2}G_{2}[\cdots]$. As a result, we obtain two relations between special values of the function $_{2}G_{2}[\cdots]$ with different parameters.

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Rupam Barman, Neelam Saikia. 2013-11-20. p-adic Gamma function and traces of Frobenius of elliptic curves. https://arxiv.org/abs/1304.3321

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