Number theoretic properties of generating functions related to Dyson’s rank for partitions into distinct parts
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- by Maria Monks PDF
- Proc. Amer. Math. Soc. 138 (2010), 481-494
Abstract:
Let $Q(n)$ denote the number of partitions of $n$ into distinct parts. We show that Dyson’s rank provides a combinatorial interpretation of the well-known fact that $Q(n)$ is almost always divisible by $4$. 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 $L$-functions at nonpositive integers.References
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Additional Information
- Maria Monks
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- ORCID: 0000-0002-0377-5501
- Email: monks@mit.edu
- 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
- © Copyright 2009 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
- MathSciNet review: 2557166