Lacunarity of certain partition-theoretic generating functions
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- by Emily Clader, Yvonne Kemper and Matt Wage PDF
- Proc. Amer. Math. Soc. 137 (2009), 2959-2968 Request permission
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.References
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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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2506454