Rank-Crank type PDE&apos;s and non-holomorphic Jacobi forms

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

Autores: Kathrin Bringmann, Sander P. Zwegers
Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 4, 2010, págs. 589-600
Idioma: inglés
DOI: 10.4310/mrl.2010.v17.n4.a1
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Resumen
- 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.