Vorono\"i summation for half-integral weight automorphic forms

TL;DR

This paper derives a general Voronoi summation formula for half-integral weight automorphic forms using a representation theoretic approach, extending classical identities to new contexts.

Contribution

It introduces a unified, representation-theoretic derivation of Voronoi summation for half-integral weight forms, broadening the scope of classical formulas.

Findings

Derived a general Voronoi summation formula for the metaplectic double cover of GL(2)

Formulated the identity both representation-theoretically and classically

Established Voronoi summation formulas for half-integral weight modular and Maass forms

Abstract

A general Vorono\"i summation formula for the (metaplectic) double cover of $\text{GL}_2$ is derived via the representation theoretic framework \`a la Ichino--Templier. The identity is also formulated classically and used to establish Vorono\"i summation formulae for half-integral weight modular forms and Maa{\ss} forms.