M_2-rank differences for overpartitions
|Title:||M_2-rank differences for overpartitions||Authors:||Lovejoy, Jeremy
|Permanent link:||http://hdl.handle.net/10197/7830||Date:||2010||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 M2-rank differences for overpartitions. Additionally, we express a third order mock theta function in terms of rank differences.||Funding Details:||Science Foundation Ireland||Type of material:||Journal Article||Publisher:||Polskiej Akademi Nauk, Instytut Matematyczny||Keywords:||Dyson's rank; M-2-rank; Rank differences; Generalized Lambert series; Modular functions; Mock theta functions; Overpartitions; Basic hypergeometric-series; Mock theta-functions; Frobenius representation; Lost notebook; Rank; Forms; Conjugation; Pairs||DOI:||10.4064/aa144-2-8||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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