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


Authors: Jenny G. Fuselier and Dermot McCarthy
Journal: Proc. Amer. Math. Soc. 144 (2016), 1493-1508
MSC (2010): Primary 11F33, 33C20; Secondary 11S80, 33E50
DOI: https://doi.org/10.1090/proc/12837
Published electronically: August 12, 2015
MathSciNet review: 3451227
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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 $ _4F_3$ hypergeometric series and the Fourier coefficients of a certain weight four modular form.


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Additional Information

Jenny G. Fuselier
Affiliation: Department of Mathematics and Computer Science, Drawer 31, High Point University, High Point, North Carolina 27268
Email: jfuselie@highpoint.edu

Dermot McCarthy
Affiliation: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79410-1042
Email: dermot.mccarthy@ttu.edu

DOI: https://doi.org/10.1090/proc/12837
Received by editor(s): July 16, 2014
Received by editor(s) in revised form: May 12, 2015
Published electronically: August 12, 2015
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2015 American Mathematical Society