On the Non-Vanishing of Poincaré Series on the Metaplectic Group

Abstract

In this paper, we study the $K$-finite matrix coefficients of integrable representations of the metaplectic cover of ${\mathrm{SL}}_2(\mathbb{R})$ and give a result on the non-vanishing of their Poincaré series. We do this by adapting the techniques developed for ${\mathrm{SL}}_2(\mathbb{R})$ by Muić to the case of the metaplectic group.

17 pages