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 seri...

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Bibliographic Details
Published inMathematical proceedings of the Cambridge Philosophical Society Vol. 168; no. 1; pp. 171 - 195
Main Authors BARMAN, RUPAM, SAIKIA, NEELAM
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 01.01.2020
Subjects
Congruences
Fields (mathematics)
Gamma function
Series (mathematics)
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Summary: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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004118000609