Congruences for some partitions related to mock theta functions
Partitions related to mock theta functions were widely studied in the literature. Recently, Andrews et al. introduced two new kinds of partitions counted by [Formula: see text] and [Formula: see text], whose generating functions are [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text] are two third mock theta functions. Meanwhile, they obtained some congruences for [Formula: see text], [Formula: see text], and the associated smallest parts function [Formula: see text]. Furthermore, Andrews et al. discussed the overpartition analogues of [Formula: see text] and [Formula: see text] which are denoted by [Formula: see text] and [Formula: see text]. In this paper, we derive more congruences for [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. Moreover, we establish some congruences for [Formula: see text] and its associated smallest parts function [Formula: see text], where [Formula: see text] denotes the number of overpartitions of [Formula: see text] such that all even parts are at most twice the smallest part, and in which the smallest part is always overlined.