\(p\)-adic gamma function and the trace of Frobenius of elliptic curves

DOI10.1016/J.JNT.2014.01.026zbMATH Open1345.11041arXiv1304.3321OpenAlexW2964229798MaRDI QIDQ401985

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Publication date: 27 August 2014

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Abstract: In cite{mccarthy2}, McCarthy defined a function ${}_n{G}_n[cdots]$ using Teichm"{u}ller 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.

Full work available at URL: https://arxiv.org/abs/1304.3321

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