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

Abstract

The problem of quantum unique ergodicity (QUE) of weight 1/2 Eisenstein series for Γ_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.

45 pages, 4 figures. Several minor corrections. To appear in Algebra and Number theory

References in corpus (1)

• Quantum Limits of Eisenstein Series and Scattering states

Cited by in corpus (2)

• Quantum Unique Ergodicity for half-integral weight forms
• A Mean Value Result for a Product of GL(2) and GL(3) L-Functions