Hypergeometric type identities in the p-adic setting and modular forms

Dermot McCarthy; Jenny Fuselier

doi:10.1090/proc/12837

Hypergeometric type identities in the p-adic setting and modular forms

Dermot McCarthy, Jenny Fuselier

Mathematics and Statistics

Research output: Contribution to journal › Article

Abstract

We prove hypergeometric type identities for a function defined in terms of quotients of the p-adic gamma function. We use these identities to prove a supercongruence conjecture of Rodriguez-Villegas between a truncated 4F3 hypergeometric series and the Fourier coefficients of certain weight four modular form.

Original language	English
Pages (from-to)	1493-1508
Journal	Proceedings of the American Mathematical Society
DOIs	https://doi.org/10.1090/proc/12837
State	Published - Apr 2016

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McCarthy, D., & Fuselier, J. (2016). Hypergeometric type identities in the p-adic setting and modular forms. Proceedings of the American Mathematical Society, 1493-1508. https://doi.org/10.1090/proc/12837

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