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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Congruences via modular forms


Authors: Robert Osburn and Brundaban Sahu
Journal: Proc. Amer. Math. Soc. 139 (2011), 2375-2381
MSC (2010): Primary 11A07; Secondary 11F11
Published electronically: December 9, 2010
MathSciNet review: 2784802
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Abstract: We prove two congruences for the coefficients of power series expansions in $ t$ of modular forms where $ t$ is a modular function. As a result, we settle two recent conjectures of Chan, Cooper and Sica. Additionally, we provide tables of congruences for numbers which appear in similar power series expansions and in the study of integral solutions of Apéry-like differential equations.


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Additional Information

Robert Osburn
Affiliation: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Email: robert.osburn@ucd.ie

Brundaban Sahu
Affiliation: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Address at time of publication: School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar 751005, India
Email: brundaban.sahu@niser.ac.in

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10771-2
PII: S 0002-9939(2010)10771-2
Keywords: Coefficients of power series expansions, congruences, modular forms
Received by editor(s): December 1, 2009
Received by editor(s) in revised form: June 29, 2010
Published electronically: December 9, 2010
Additional Notes: The authors were partially supported by Science Foundation Ireland 08/RFP/MTH1081.
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.