The Weyl bound for triple product L-functions

Abstract

Let π1, π2, π3 be three cuspidal automorphic representations for the group SL(2,Z), where π1 and π2 are fixed and π3 has large analytic conductor. We prove a subconvex bound for L(1∕2,π1⊗π2⊗π3) of Weyl-type quality. Allowing π3 to be an Eisenstein series, we also obtain a Weyl-type subconvex bound for L(1∕2+it,π1⊗π2).