The Lewis Correspondence for submodular groups

TL;DR

This paper extends the Lewis Correspondence, which links Maass wave forms to period functions, to subgroups of finite index using vector-valued forms, broadening its applicability.

Contribution

It introduces a method to generalize the Lewis Correspondence to subgroups of finite index via vector-valued forms, expanding the theoretical framework.

Findings

Extended Lewis Correspondence to subgroups of finite index

Utilized vector-valued forms for the generalization

Established a unique period function for each Maass wave form

Abstract

The Lewis Correspondence attaching a unique "period function" to each Maass wave form for SL(2,Z) is extended to subgroups of finite index. This is achieved by using vector-valued forms.