Shintani correspondence for Maass forms of level $N$ and prehomogeneous zeta functions

TL;DR

This paper establishes a Shintani correspondence for Maass cusp forms of level N by linking it to the analytic properties of prehomogeneous zeta functions involving periods of these forms.

Contribution

It introduces a novel connection between Maass forms and prehomogeneous zeta functions, extending the Shintani correspondence to higher levels.

Findings

Derived a Shintani-Katok-Sarnak type correspondence for level N Maass forms

Linked Maass form periods to prehomogeneous zeta function coefficients

Showed analytic properties of zeta functions encode Maass form symmetries

Abstract

A Shintani-Katok-Sarnak type correspondence for Maass cusp forms of level $N$ is shown to be derived from analytic properties of prehomogeneous zeta functions whose coefficients involve periods of Maass forms.