English

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}
}
R2 v1 2026-06-21T11:03:21.892Z