Maass waveforms arising from sigma and related indefinite theta functions

TL;DR

This paper explores a specific Maass waveform derived from functions related to sigma, expanding understanding of their structure within a broader mathematical framework.

Contribution

It generalizes a known Maass waveform example from sigma functions, providing a new framework for analyzing such waveforms.

Findings

Identifies a new class of Maass waveforms linked to sigma functions

Provides a generalized framework for these waveforms

Connects classical functions to modern Maass form theory

Abstract

In this paper we consider an example of a Maass waveform which was constructed by Cohen from a function $\sigma$, studied by Andrews, Dyson and Hickerson, and it's companion $\sigma^*$. We put this example in a more general framework.