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Supercongruences for truncated hypergeometric series and p-adic gamma function

Published online by Cambridge University Press:  10 August 2018

RUPAM BARMAN  and
NEELAM SAIKIA
RUPAM BARMAN
Affiliation:
Department of Mathematics, Indian Institute of Technology Guwahati, North Guwahati, Guwahati-781039, Assam, India. e-mail: [email protected], [email protected]
NEELAM SAIKIA
Affiliation:
Department of Mathematics, Indian Institute of Technology Guwahati, North Guwahati, Guwahati-781039, Assam, India. e-mail: [email protected], [email protected]
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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 7F6 truncated hypergeometric series which is similar to a supercongruence proved by L. Long and R. Ramakrishna.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 1 , January 2020 , pp. 171 - 195
Copyright
Copyright © Cambridge Philosophical Society 2018 

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