Generalized Maass Wave Forms

TL;DR

This paper introduces generalized Maass wave forms with non-unitary multipliers, extending classical theory and establishing foundational theorems for this broader class of automorphic forms.

Contribution

It pioneers the study of non-unitary multiplier systems in Maass wave forms, broadening the scope of automorphic form theory.

Findings

Basic theorems from classical Maass forms are generalized.

Examples from classical theory are extended to the generalized setting.

Foundational properties of generalized Maass wave forms are established.

Abstract

We initiate the study of generalized Maass wave forms, those Maass wave forms for which the multiplier system is not necessarily unitary. We then prove some basic theorems inherited from the classical theory of modular forms with a generalization of some examples from the classical theory of Maass forms.