Mock theta functions and indefinite modular forms II

TL;DR

This paper investigates the modular properties of indefinite modular forms related to mock theta functions, specifically computing Zwegers's modifications and analyzing their transformation behaviors.

Contribution

It provides explicit computations of Zwegers's modifications of mock theta functions and studies their modular transformation properties, advancing understanding of their structure.

Findings

Explicit formulas for Zwegers's modifications of mock theta functions

Analysis of modular transformation properties of indefinite modular forms

Enhanced understanding of the structure of modified mock theta functions

Abstract

In this paper, we compute the Zwegers's modification of the mock theta functions $\Phi^{[m,0] \, \ast}$ and study the modular transformation properties of the indefinite modular forms which appear in the explicit formula for the modified functions $\tilde{\Phi}^{[m,0] \, \ast}$.