Mathematical Research Letters

Volume 17 (2010)

Number 4

Rank-Crank type PDE’s and non-holomorphic Jacobi forms

Pages: 589 – 600



Kathrin Bringmann (Mathematical Institute, University of Cologne, Germany)

Sander Zwegers (School of Mathematical Sciences, University College Dublin, Ireland)


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.

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