Hybrid subconvexity bounds for L(1/2,Sym²f⊗g)

Abstract

Fix an integer κ⩾2. Let P be prime and let k>κ be an even integer. For f a holomorphic cusp form of weight k and full level and g a primitive holomorphic cusp form of weight 2κ and level P, we prove hybrid subconvexity bounds for L(1/2, Sym²f⊗g) in the k and P aspects when P^13/64+δ<k<P^3/8−δ for any 0<δ<11/128. These bounds are achieved through a first moment method (with amplification when P^13/64<k⩽P413).