Overpartition rank differences modulo 7 by Maass forms

JOURNAL OF NUMBER THEORY

卷:163

Article

Jennings-Shaffer, C.¹ 

[1] Oregon State Univ, Dept Math, Corvallis, OR 97331 USA

关键词: Number theory;    Partitions;    Overpartitions;    Ranks;    Rank differences;    Maass forms;    Modular forms;   

DOI  :  10.1016/j.jnt.2015.11.018

来源: Elsevier

【 摘 要 】

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 SL2 (Z) as well as formulas for orders at cusps. (c) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free