Generating Functions and Congruences for Some Partition Functions Related to Mock Theta Functions

Abstract

Recently, Andrews, Dixit and Yee introduced partition functions associated with Ramanujan/Watson third order mock theta functions $\omega (q)$ and $\nu (q)$. In this paper, we find several new exact generating functions for those partition functions as well as the associated smallest parts functions and deduce several new congruences modulo powers of 5.

23 pages