Number theoretic properties of generating functions related to Dyson's rank for partitions into distinct parts

Author:
Maria Monks

Journal:
Proc. Amer. Math. Soc. **138** (2010), 481-494

MSC (2000):
Primary 11P82, 11P83

DOI:
https://doi.org/10.1090/S0002-9939-09-10076-X

Published electronically:
September 10, 2009

MathSciNet review:
2557166

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the number of partitions of into distinct parts. We show that Dyson's rank provides a combinatorial interpretation of the well-known fact that is almost always divisible by . This interpretation gives rise to a new false theta function identity that reveals surprising analytic properties of one of Ramanujan's mock theta functions, which in turn gives generating functions for values of certain Dirichlet -functions at nonpositive integers.

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Additional Information

**Maria Monks**

Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Email:
monks@mit.edu

DOI:
https://doi.org/10.1090/S0002-9939-09-10076-X

Received by editor(s):
April 20, 2009

Received by editor(s) in revised form:
June 7, 2009

Published electronically:
September 10, 2009

Communicated by:
Ken Ono

Article copyright:
© Copyright 2009
Maria Monks