Hypergeometric type identities in the -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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We prove hypergeometric type identities for a function defined in terms of quotients of the -adic gamma function. We use these identities to prove a supercongruence conjecture of Rodriguez-Villegas between a truncated
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