Automorphic properties of generating functions for generalized rank moments and Durfee

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 special-izations 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 automor-phic properties are deduced using q-series identities relating the relevant generating functions to known mock theta functions. 1