Automorphic properties of generating functions for generalized rank moments and Durfee symbols
Kathrin Bringmann, Jeremy Lovejoy, and Robert Osburn
Arxiv ID: 0802.3277•Last updated: 2/3/2021
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.
PaperStudio AI Chat
I'm your research assistant! Ask me anything about this paper.