Period functions for Maass cusp forms for $\Gamma_0(p)$: a transfer operator approach

TL;DR

This paper introduces a transfer operator approach to characterize Maass cusp forms for Hecke congruence subgroups of prime level as eigenfunctions, providing a new analytical framework.

Contribution

It develops a transfer operator method to analyze Maass cusp forms for $\Gamma_0(p)$, offering a novel perspective compared to traditional techniques.

Findings

Maass cusp forms are characterized as 1-eigenfunctions of a finite transfer operator.

The approach simplifies the analysis of cusp forms for prime level groups.

Provides a new tool for studying automorphic forms via transfer operators.

Abstract

We characterize the Maass cusp forms for Hecke congruence subgroups of prime level as 1-eigenfunctions of a finite-term transfer operator.