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