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

Dermot McCarthy; Jenny Fuselier

doi:10.1090/proc/12837

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

Dermot McCarthy, Jenny Fuselier

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1493-1508
Journal	Proceedings of the American Mathematical Society
DOIs	https://doi.org/10.1090/proc/12837
State	Published - Apr 2016

Access to Document

10.1090/proc/12837

Fingerprint Dive into the research topics of 'Hypergeometric type identities in the p-adic setting and modular forms'. Together they form a unique fingerprint.

Cite this

@article{7c2bfb1521aa46c8adee016e2c3b49f8,

title = "Hypergeometric type identities in the p-adic setting and modular forms",

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.",

author = "Dermot McCarthy and Jenny Fuselier",

year = "2016",

month = apr,

doi = "10.1090/proc/12837",

language = "English",

pages = "1493--1508",

journal = "Proceedings of the American Mathematical Society",

}

TY - JOUR

T1 - Hypergeometric type identities in the p-adic setting and modular forms

AU - McCarthy, Dermot

AU - Fuselier, Jenny

PY - 2016/4

Y1 - 2016/4

N2 - 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.

AB - 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.

U2 - 10.1090/proc/12837

DO - 10.1090/proc/12837

M3 - Article

SP - 1493

EP - 1508

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

ER -