Rank differences for overpartitions
|Title:||Rank differences for overpartitions||Authors:||Lovejoy, Jeremy
|Permanent link:||http://hdl.handle.net/10197/7946||Date:||2-Jun-2008||Online since:||2016-09-15T16:13:21Z||Abstract:||In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures on the rank of a partition by establishing formulae for the generating functions for rank differences in arithmetic progressions. In this paper, we prove formulae for the generating functions for rank differences for overpartitions. These are in terms of modular functions and generalized Lambert series.||Type of material:||Journal Article||Publisher:||Oxford University Press||Journal:||Quarterly Journal of Mathematics||Volume:||59||Issue:||2||Start page:||257||End page:||273||Copyright (published version):||2008 Oxford University Press||Keywords:||Elementary theory of partitions; Partitions of integers||DOI:||10.1093/qmath/ham031||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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