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arxiv: 1507.07391 · v5 · pith:BPNIMWFYnew · submitted 2015-07-27 · 🧮 math.NT

Supercongruences for truncated hypergeometric series and p-adic gamma function

classification 🧮 math.NT
keywords hypergeometricseriessupercongruencessupercongruencetruncatedfunctiongammageneral
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We prove three more general supercongruences between truncated hypergeometric series and $p$-adic Gamma function from which some known supercongruences follow. A supercongruence conjectured by Rodriguez-Villegas and proved by E. Mortenson using the theory of finite field hypergeometric series follows from one of our more general supercongruences. We also prove a supercongruence for ${_7}F_6$ truncated hypergeometric series which is similar to a supercongruence proved by L. Long and R. Ramakrishna.

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