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

DOI:
https://doi.org/10.1090/S0002-9939-2010-10771-2

Published electronically:
December 9, 2010

MathSciNet review:
2784802

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove two congruences for the coefficients of power series expansions in of modular forms where 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:
https://doi.org/10.1090/S0002-9939-2010-10771-2

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.