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

Fuselier, Jenny; McCarthy, Dermot

doi:10.1090/proc/12837

Hypergeometric type identities in the $p$-adic setting and modular forms
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by Jenny G. Fuselier and Dermot McCarthy PDF

Proc. Amer. Math. Soc. 144 (2016), 1493-1508 Request permission

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 $_4F_3$ hypergeometric series and the Fourier coefficients of a certain weight four modular form.

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