  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.
