On certain explicit congruences for mock theta functions

TL;DR

This paper provides the first explicit examples of congruences for Ramanujan's mock theta functions, expanding understanding of their arithmetic properties and building on recent discoveries of Ramanujan-type congruences.

Contribution

It introduces the first explicit congruences for the mock theta functions  and , advancing the study of their arithmetic behavior.

Findings

Explicit congruences for  and  are established.

The work extends Ramanujan-type congruence results to mock theta functions.

Provides new tools for analyzing mock theta function coefficients.

Abstract

Recently, Garthwaite-Penniston have shown that the coefficients of Ramanujan's mock theta function $\omega$ satisfy infinitely many congruences of Ramanujan-type. In this work we give the first explicit examples of congruences for Ramanujan's mock theta function $\omega$ and another mock theta function $\mathcal{C}$.