M_2-rank differences for overpartitions

Abstract

This is the third and final installment in our series of papers applying the method of Atkin and Swinnerton-Dyer to deduce formulas for rank differences. The study of rank differences was initiated by Atkin and Swinnerton-Dyer in their proof of Dyson's conjectures concerning Ramanujan's congruences for the partition function. Since then, other types of rank differences for statistics associated to partitions have been investigated. In this paper, we prove explicit formulas for M_2-rank differences for overpartitions. Additionally, we express a third order mock theta function in terms of rank differences.

19 pages

References in corpus (1)

• M_2-rank differences for partitions without repeated odd parts

Cited by in corpus (7)

• Dyson's Ranks and Appell-Lerch Sums
• Variations of Andrews-Beck type congruences
• The Unimodality of the Crank on Overpartitions
• On recursions for coefficients of mock theta functions
• Combinatorial Interpretations of Cranks of Overpartitions and Partitions without Repeated Odd Parts
• Monotonicity properties for ranks of overpartitions
• Rank deviations for overpartitions