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arxiv: 1802.04503 · v1 · pith:M7FB4XPCnew · submitted 2018-02-13 · 🧮 math.NT

Certain character sums and hypergeometric series

classification 🧮 math.NT
keywords hypergeometricadicseriestransformationcharactersumstransformationsanalogues
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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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