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arXiv · 0802.3277

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

Kathrin Bringmann·Jeremy Lovejoy·Robert Osburn
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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.

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Kathrin Bringmann, Jeremy Lovejoy, Robert Osburn. 2008-02-22. Automorphic properties of generating functions for generalized rank moments and Durfee symbols. https://doi.org/10.1093/imrn%2Frnp131

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