Mock theta functions and weakly holomorphic modular forms modulo 2 and 3

TL;DR

This paper investigates the congruence properties of mock theta functions and weakly holomorphic modular forms modulo 2 and 3, revealing the absence of linear congruences and extending previous results on partition functions.

Contribution

It establishes new non-congruence results for mock theta functions and weakly holomorphic modular forms modulo 2 and 3, expanding the understanding of their arithmetic properties.

Findings

Coefficients of certain mock theta functions have no linear congruences modulo 3.

Similar non-congruence results are proved for a broad class of weakly holomorphic modular forms.

The work extends Radu's results on the partition function modulo 2 and 3.

Abstract

We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications. This extends work of Radu on the behavior of the ordinary partition function modulo 2 and 3.