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

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

2008-02-22

arxiv.org/abs/0802.3277v1

IMRN, no. 2, (2010), 238-260

Mathematics

Number Theory

18 pages

Scientific paper

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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