Lewis-Zagier correspondence for higher order forms

TL;DR

This paper extends the Lewis-Zagier correspondence to higher order Maaß wave forms by identifying higher order invariants with unipotent twists, enabling the use of standard automorphic form techniques.

Contribution

It introduces a novel approach to relate higher order invariants to ordinary invariants, broadening the applicability of the Lewis-Zagier correspondence.

Findings

Extended the Lewis-Zagier correspondence to higher order forms

Identified higher order invariants with unipotent twists

Enabled application of standard automorphic methods to higher order forms

Abstract

The Lewis-Zagier correspondence, which attaches period functions to Maa\ss\ wave forms, is extended to wave forms of higher order, which are higher invariants of the Fuchsian group in question. The key ingredient is an identification of Higher order invariants with ordinary invariants of unipotent twists. This makes it possible to apply standard methods of automorphic forms to higher order forms.