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Lacunarity of certain partition-theoretic generating functions

Authors: Emily Clader, Yvonne Kemper and Matt Wage
Journal: Proc. Amer. Math. Soc. 137 (2009), 2959-2968
MSC (2000): Primary 11F30, 11P82, 11F11; Secondary 11F20
Published electronically: May 6, 2009
MathSciNet review: 2506454
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a certain family of infinite products, denoted $ f_{a,b}$, which were introduced by Han as a generalization of the Nekrasov-Okounkov formula. Extending the work of Serre on powers of Dedekind's $ \eta$-function, we investigate the integers $ a$ and $ b$ for which ``almost all'' of the Fourier coefficients of $ f_{a,b}$ are zero (forms with this property are referred to as lacunary). We give the complete list of pairs $ (a,b)$, where $ b$ is odd, for which $ f_{a,b}$ is lacunary.

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Additional Information

Emily Clader
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027

Yvonne Kemper
Affiliation: Department of Mathematics, University of California Berkeley, Berkeley, California 94708

Matt Wage
Affiliation: Appleton East High School, 1411 N. Briarcliff Drive, Appleton, Wisconsin 54915
Address at time of publication: Princeton University, 0920 Frist Campus Center, Princeton, New Jersey 08544

Received by editor(s): July 31, 2008
Received by editor(s) in revised form: January 19, 2009
Published electronically: May 6, 2009
Communicated by: Jim Haglund
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.