Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11F30, 11P82, 11F11, 11F20

Retrieve articles in all journals with MSC (2000): 11F30, 11P82, 11F11, 11F20


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/S0002-9939-09-09896-7
PII: S 0002-9939(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.