Double Dirichlet series and quantum unique ergodicity of weight 1/2 Eisenstein series

TL;DR

This paper investigates the quantum unique ergodicity of weight 1/2 Eisenstein series by analyzing associated double Dirichlet series, establishing that subconvex bounds imply QUE for these automorphic forms.

Contribution

It introduces a novel connection between double Dirichlet series properties and quantum unique ergodicity for half-integer weight Eisenstein series.

Findings

Analytic continuation and convexity estimates for the double Dirichlet series

Subconvex bounds imply QUE for weight 1/2 Eisenstein series

New insights into automorphic forms and Dirichlet series connection

Abstract

The problem of quantum unique ergodicity (QUE) of weight 1/2 Eisenstein series for {\Gamma}_0(4) leads to the study of certain double Dirichlet series involving GL2 automorphic forms and Dirichlet characters. We study the analytic properties of this family of double Dirichlet series (analytic continuation, convexity estimate) and prove that a subconvex estimate implies the QUE result.