A characterization of modified mock theta functions

TL;DR

This paper characterizes modified mock theta functions, as defined by Zwegers, by their analytic, elliptic, and differential properties, paralleling the classical theta functions.

Contribution

It provides a new characterization of modified mock theta functions based on their transformation and differential properties, extending the classical theory.

Findings

Modified mock theta functions are characterized by their analyticity and elliptic transformation properties.

They are uniquely identified by being annihilated by specific second order differential operators.

The characterization parallels that of ordinary theta functions.

Abstract

We give a characterization of modified (in the sense of Zwegers) mock theta functions, parallel to that of ordinary theta functions. Namely, modified mock theta functions are characterized by their analyticity properties, elliptic transformation properties, and by being annihilated by certain second order differential operators.