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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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