Supercongruences for truncated hypergeometric series and p-adic gamma function

Abstract

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.

To appear in Mathematical Proceedings Cambridge Phil. Soc

References in corpus (2)

• Supercongruences for sporadic sequences
• On the supercongruence conjectures of van Hamme

Cited by in corpus (2)

• $p$-adic analogues of hypergeometric identities
• Some Numeric Hypergeometric Supercongruences