Mixed mock modular q-series

TL;DR

This survey explores mixed mock modular q-series, which combine mock modular forms and modular forms, highlighting their prevalence and various ways they arise in mathematical contexts.

Contribution

It provides an overview of how mixed mock modular q-series emerge and their significance in the study of modular forms.

Findings

Mixed mock modular forms are more common than mock theta functions.

They appear as q-hypergeometric series in various mathematical contexts.

The survey discusses different methods of their emergence.

Abstract

Mixed mock modular forms are functions which lie in the tensor space of mock modular forms and modular forms. As q-hypergeometric series, mixed mock modular forms appear to be much more common than mock theta functions. In this survey, we discuss some of the ways such series arise.