Lacunarity of certain partitiontheoretic generating functions
Authors:
Emily Clader, Yvonne Kemper and Matt Wage
Journal:
Proc. Amer. Math. Soc. 137 (2009), 29592968
MSC (2000):
Primary 11F30, 11P82, 11F11; Secondary 11F20
Published electronically:
May 6, 2009
MathSciNet review:
2506454
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Abstract: We consider a certain family of infinite products, denoted , which were introduced by Han as a generalization of the NekrasovOkounkov 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:
http://dx.doi.org/10.1090/S0002993909098967
PII:
S 00029939(09)098967
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.
