Rank and crank moments for overpartitions

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Title: Rank and crank moments for overpartitions
Authors: Bringmann, Kathrin
Lovejoy, Jeremy
Osburn, Robert
Permanent link: http://hdl.handle.net/10197/7955
Date: Jul-2009
Online since: 2016-09-16T11:13:34Z
Abstract: We study two types of crank moments and two types of rank moments for overpartitions. We show that the crank moments and their derivatives, along with certain linear combinations of the rank moments and their derivatives, can be written in terms of quasimodular forms. We then use this fact to prove exact relations involving the moments as well as congruence properties modulo 3, 5, and 7 for some combinatorial functions which may be expressed in terms of the second moments. Finally, we establish a congruence modulo 3 involving one such combinatorial function and the Hurwitz class number H(n).
Type of material: Journal Article
Publisher: Elsevier
Journal: Journal of Number Theory
Volume: 129
Issue: 7
Start page: 1758
End page: 1772
Copyright (published version): 2008 Elsevier
Keywords: Holomorphic modular forms of integral weightPartitionsCongruencesCongruential restrictions
DOI: 10.1016/j.jnt.2008.10.017
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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