Overpartition Rank Differences Modulo 7 By Maass Forms

Chris Jennings-Shaffer

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arXiv · 1601.06671

Overpartition Rank Differences Modulo 7 By Maass Forms

Chris Jennings-Shaffer

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Abstract

Using that the overpartition rank function is the holomorphic part of a harmonic Maass form, we deduce formulas for the rank differences modulo 7. To do so we make improvements on the current state of the overpartition rank function in terms of harmonic Maass forms by giving simple formulas for the transformations under $\mbox{SL}_2(\mathbb{Z})$ as well as formulas for orders at cusps.

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Chris Jennings-Shaffer. 2016-01-25. Overpartition Rank Differences Modulo 7 By Maass Forms. https://arxiv.org/abs/1601.06671

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