Uniform subconvexity bounds for GL(2)× GL(2) L-functions in the spectral aspect

In this paper, we study the second moment for GL(2)× GL(2) L-functions L(1/2,f× g), which leads to a uniform subconvexity bound in the spectral aspect. In particular, if either f or g is a dihedral Maass newform, or if one of them has level $1$, we obtain a Burgess-type bound that is uniform in both tf and tg, where tf, tg denote the spectral parameters of f, g. As an application, we also establish a shrinking result for QUE in the case of dihedral Maass newforms.