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

2014/07/24 by Jenny G. Fuselier, Fuselier, Jenny G., Dermot McCarthy +1 · 1 citation
Mathematics · #33C20 #33E50 #FOS: Mathematics #Number Theory (math.NT) #Primary: 11F33 #Secondary: 11S80 #math.NT #msc:11F33 #msc:11S80 #msc:33C20 #msc:33E50

paper · pdf · doi:10.48550/arxiv.1407.6670

arxiv created 2014/07/24 · arxiv updated 2014/07/25

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.

Cited by

• The Explicit Hypergeometric Modularity Method III

Related

• p-Adic hypergeometric functions and certain weight three newforms
• Supercongruences involving p-adic Gamma functions
• p-adic analogues of hypergeometric identities
• Supercongruences between truncated ₃F₂ hypergeometric series
• Supercongruences for truncated hypergeometric series and p-adic gamma\n function