Automorphic properties of generating functions for generalized rank moments and Durfee symbols

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Title: Automorphic properties of generating functions for generalized rank moments and Durfee symbols
Authors: Bringmann, Kathrin
Lovejoy, Jeremy
Osburn, Robert
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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 integersModular functionsAutomorphic 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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