Twisted moments of L-functions and spectral reciprocity

Abstract

We establish a reciprocity formula that expresses the fourth moment of automorphic L-functions of level q twisted by the ℓth Hecke eigenvalue as the fourth moment of automorphic L-functions of level ℓ twisted by the qth Hecke eigenvalue. Direct corollaries include subconvexity bounds for L-functions in the level aspect and a short proof of an upper bound for the fifth moment of automorphic L-functions.