Automorphic properties of generating functions for generalized rank moments and Durfee symbols
|Title:||Automorphic properties of generating functions for generalized rank moments and Durfee symbols||Authors:||Bringmann, Kathrin
|Permanent link:||http://hdl.handle.net/10197/7822||Date:||2010||Abstract:||We define two-parameter generalizations of two combinatorial constructions of Andrews: the kth symmetrized rank moment and the k-marked Durfee symbol. We prove that three specializations of the associated generating functions are so-called quasimock theta functions, while a fourth specialization gives quasimodular forms. We then define a two-parameter generalization of Andrews' smallest parts function and note that this leads to quasimock theta functions as well. The automorphic properties are deduced using q-series identities relating the relevant generating functions to known mock theta functions.||Funding Details:||Science Foundation Ireland||Type of material:||Journal Article||Publisher:||Elsevier||Journal:||International Mathematics Research Notices||Issue:||2||Start page:||238||End page:||260||Copyright (published version):||2009 the Authors||Keywords:||Partitions of integers; Modular functions; Automorphic functions||DOI:||10.1093/imrn/rnp131||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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