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

DOI10.1090/PROC/12837zbMATH Open1397.11078arXiv1407.6670OpenAlexW2963479063MaRDI QIDQ2790258

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Publication date: 3 March 2016

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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 ${}_4{F}_3$ hypergeometric series and the Fourier coefficients of certain weight four modular form.

Full work available at URL: https://arxiv.org/abs/1407.6670

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