# Overpartition Rank Differences Modulo 7 By Maass Forms

Research paper by Chris Jennings-Shaffer

Indexed on: 25 Jan '16Published on: 25 Jan '16Published in: Mathematics - Number Theory

#### 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.