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Sequences, modular forms and cellular integrals

Published online by Cambridge University Press:  11 October 2018

DERMOT McCARTHY ,
ROBERT OSBURN  and
ARMIN STRAUB
DERMOT McCARTHY
Affiliation:
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79410-1042, U.S.A. e-mail: dermot.mccarthy@ttu.edu
ROBERT OSBURN
Affiliation:
School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland. e-mail: robert.osburn@ucd.ie
ARMIN STRAUB
Affiliation:
Department of Mathematics and Statistics, University of South Alabama. 411 University Blvd N, MSPB 325, Mobile AL 36686, U.S.A. e-mail: straub@southalabama.edu
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Abstract

It is well-known that the Apéry sequences which arise in the irrationality proofs for ζ(2) and ζ(3) satisfy many intriguing arithmetic properties and are related to the pth Fourier coefficients of modular forms. In this paper, we prove that the connection to modular forms persists for sequences associated to Brown's cellular integrals and state a general conjecture concerning supercongruences.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 2 , March 2020 , pp. 379 - 404
Copyright
Copyright © Cambridge Philosophical Society 2018 

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