Mock modularity of the M_d-rank of overpartitions

2017/06/01 by Chris Jennings-Shaffer, Jennings-Shaffer, Chris, Holly Swisher +1 · 1 citation
Mathematics · #11F37 #33D99 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary 11P82 #Secondary 11P81

paper · doi:10.48550/arxiv.1706.00521

openalex publication_date 2017/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the modular properties of a new partition rank, the M_d-rank of overpartitions. In fact this is an infinite family of ranks, indexed by the positive integer d, that gives both the Dyson rank of overpartitions and the overpartition M₂-rank as special cases. The M_d-rank of overpartitions is the holomorphic part of a certain harmonic Maass form of weight (1)/(2). We give the exact transformation of this harmonic Maass form along with a few identities for the M_d-rank.

Cited by

• Generalized rank deviations for overpartitions

Related

• Dyson's Rank, overpartitions, and weak Maass forms
• The generating function of the M₂-rank of partitions without repeated\n odd parts as a mock modular form
• Generalizations of Dyson's Rank on Overpartitions
• A new approach to the Dyson rank conjectures
• Dyson’s ranks and Maass forms