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arXiv · 1802.04503

Certain character sums and hypergeometric series

Rupam Barman·Neelam Saikia
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Abstract

We prove two transformations for the $p$-adic hypergeometric series which can be described as $p$-adic analogues of a Kummer's linear transformation and a transformation of Clausen. We first evaluate two character sums, and then relate them to the $p$-adic hypergeometric series to deduce the transformations. We also find another transformation for the $p$-adic hypergeometric series from which many special values of the $p$-adic hypergeometric series as well as finite field hypergeometric functions are obtained.

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Rupam Barman, Neelam Saikia. 2018-02-13. Certain character sums and hypergeometric series. https://arxiv.org/abs/1802.04503

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