Dyson's Rank, overpartitions, and weak Maass forms

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dc.creatorBringmann, Kathrin
dc.creatorLovejoy, Jeremy
dc.date2007-08-05
dc.date.accessioned2026-07-07T08:22:17Z
dc.date.available2026-07-07T08:22:17Z
dc.descriptionIn a series of papers the first author and Ono connected the rank, a partition statistic introduced by Dyson, to weak Maass forms, a new class of functions which are related to modular forms. Naturally it is of wide interest to find other explicit examples of Maass forms. Here we construct a new infinite family of such forms, arising from overpartitions. As applications we obtain combinatorial decompositions of Ramanujan-type congruences for overpartitions as well as the modularity of rank differences in certain arithmetic progressions.
dc.description24 pages IMRN, accepted for publication
dc.identifierhttps://arxiv.org/abs/0708.0692
dc.identifierhttp://arxiv.org/abs/0708.0692
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/135602
dc.subjectNumber Theory
dc.subject11P82, 05A17
dc.titleDyson's Rank, overpartitions, and weak Maass forms
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