Congruences modulo powers of 5 for the rank parity function

TL;DR

This paper proves new congruences modulo powers of 5 for the rank parity function, a mock theta function related to partition theory, extending known results for related functions.

Contribution

It establishes the first known congruences modulo powers of 5 for the rank parity function, a mock theta function mentioned by Ramanujan.

Findings

Proves congruences modulo powers of 5 for the rank parity function.

Extends the understanding of congruences for mock theta functions.

Connects to classical results on partition functions and their congruences.

Abstract

It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 and and 11 for the partition function. These were subsequently proved by Watson (1938) and Atkin (1967). In 2009 Choi, Kang, and Lovejoy proved congruences modulo powers of 5 for the crank parity function. The generating function for rank parity function is f(q), which is the first example of a mock theta function that Ramanujan mentioned in his last letter to Hardy. We prove congruences modulo powers of 5 for the rank parity function.