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

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

2008-07-23

arxiv.org/abs/0807.3603v1

Mathematics

Number Theory

Scientific paper

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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