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

TL;DR

This paper derives new generating functions and congruences modulo powers of 5 for partition functions related to Ramanujan's third order mock theta functions, expanding understanding of their arithmetic properties.

Contribution

It introduces new exact generating functions for these partition functions and their smallest parts functions, along with novel congruences modulo powers of 5.

Findings

New generating functions for partition functions related to mock theta functions

Congruences modulo powers of 5 for these partition functions

Enhanced understanding of their arithmetic properties

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.