Rank and crank moments for overpartitions
|Title:||Rank and crank moments for overpartitions||Authors:||Bringmann, Kathrin
|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 weight; Partitions; Congruences; Congruential 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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