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)

   

 

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
Published electronically: September 10, 2009
MathSciNet review: 2557166
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11P82, 11P83

Retrieve articles in all journals with MSC (2000): 11P82, 11P83


Additional Information

Maria Monks
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: monks@mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10076-X
PII: S 0002-9939(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