M_2-rank differences for overpartitions

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Title: M_2-rank differences for overpartitions
Authors: Lovejoy, Jeremy
Osburn, Robert
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 rankM-2-rankRank differencesGeneralized Lambert seriesModular functionsMock theta functionsOverpartitionsBasic hypergeometric-seriesMock theta-functionsFrobenius representationLost notebookRankFormsConjugationPairs
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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