Voronoï summation for half-integral weight automorphic forms

Abstract

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

Minor modifications