Rank-Crank type PDE's and non-holomorphic Jacobi forms
Number Theory
2008-07-24 v1 Combinatorics
Abstract
In this paper we show how Rank-Crank type PDE's (first found by Atkin and Garvan) occur naturally in the framework of non-holomorphic Jacobiforms and find an infinite family of such differential equations. As an application we show an infinite family of congruences for odd Durfee symbols, a partition statistic introduced by George Andrews.
Cite
@article{arxiv.0807.3603,
title = {Rank-Crank type PDE's and non-holomorphic Jacobi forms},
author = {Kathrin Bringmann and Sander Zwegers},
journal= {arXiv preprint arXiv:0807.3603},
year = {2008}
}