Certain character sums and hypergeometric series

DOI10.2140/PJM.2018.295.271zbMATH Open1442.11162arXiv1802.04503OpenAlexW2963622984WikidataQ129959596 ScholiaQ129959596MaRDI QIDQ1744250

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Publication date: 23 April 2018

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1802.04503

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