Summation identities and special values of hypergeometric series in the $p$-adic setting

Rupam Barman; Neelam Saikia; Dermot McCarthy

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arXiv · 1408.5003

Summation identities and special values of hypergeometric series in the $p$-adic setting

Rupam Barman·Neelam Saikia·Dermot McCarthy

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Abstract

We prove hypergeometric type summation identities for a function defined in terms of quotients of the $p$-adic gamma function by counting points on certain families of hyperelliptic curves over $\mathbb{F}_{q}$. We also find certain special values of that function.

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Rupam Barman, Neelam Saikia, Dermot McCarthy. 2014-08-21. Summation identities and special values of hypergeometric series in the $p$-adic setting. https://arxiv.org/abs/1408.5003

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