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

DOI:
https://doi.org/10.1090/S0002-9939-09-09896-7

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 , which were introduced by Han as a generalization of the Nekrasov-Okounkov formula. Extending the work of Serre on powers of Dedekind's -function, we investigate the integers and for which ``almost all'' of the Fourier coefficients of are zero (forms with this property are referred to as lacunary). We give the complete list of pairs , where is odd, for which 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

DOI:
https://doi.org/10.1090/S0002-9939-09-09896-7

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.