We discuss the nonvanishing of the family of central values L( 1 2 , f ⊗ χ), where f is a fixed automorphic form on GL(2) and χ varies through class group characters of an imaginary quadratic field K = Q( √ −D), as D varies; we prove results of the nature that at least D1/5000 such twists are nonvanishing. We also discuss the related question of the rank of a fixed elliptic curve E/Q over the H...

Given a pair of distinct unitary cuspidal automorphic representations for GL([Formula: see text]) over number field, let [Formula: text] denote the set finite places at which are unramified and their associated Hecke eigenvalues differ. In this paper, we demonstrate how conjectures on automorphy possible cuspidality adjoint lifts Rankin–Selberg products imply lower bounds size text]. We also ob...

This is a joint work with Yangbo Ye. We prove a subconvexity bound for Rankin-Selberg L-functions L(s, f⊗g) associated with a Maass cusp form f and a fixed cusp form g in the aspect of the Laplace eigenvalue 1/4 + k2 of f , on the critical line Res = 1/2. Using this subconvexity bound, we prove the equidistribution conjecture of Rudnick and Sarnak on quantum unique ergodicity for dihedral Maass...