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CONGRUENCES FOR THE COEFFICIENTS OF WEAKLY HOLOMORPHIC MODULAR FORMS

Published online by Cambridge University Press:  07 August 2006

STEPHANIE TRENEER
STEPHANIE TRENEER
Affiliation:
Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, IL 61801, USAtreneer@math.uiuc.edu
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Abstract

Recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. We show that this type of phenomenon is completely general, by finding similar congruences for the coefficients of any weakly holomorphic modular form on any congruence subgroup $\Gamma_0 (N)$. In particular, we give congruences for a wide class of partition functions and for traces of CM values of arbitrary modular functions on certain congruence subgroups of prime level.

Keywords

11F37 (primary)11F33 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 93 , Issue 2 , September 2006 , pp. 304 - 324
Copyright
2006 London Mathematical Society

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