Explicit congruences for mock modular forms

TL;DR

This paper establishes explicit congruences for p-adic modular forms derived from mock modular forms, advancing understanding of their arithmetic properties and connections.

Contribution

It provides the first explicit congruences for p-adic modular forms constructed from mock modular forms, enhancing the theoretical framework.

Findings

Explicit congruences for p-adic modular forms are proven.

The results deepen the understanding of mock modular forms' arithmetic properties.

Connections between mock and p-adic modular forms are clarified.

Abstract

In recent work of Bringmann, Guerzhoy, and the first author, p-adic modular forms were constructed from mock modular forms. This paper proves explicit congruences for these p-adic modular forms.