A Twisted Motohashi Formula and Weyl-Subconvexity for L-functions of Weight Two Cusp Forms
Abstract
We derive a Motohashi-type formula for the cubic moment of central values of L-functions of level q cusp forms twisted by quadratic characters of conductor q, previously studied by Conrey and Iwaniec and Young. Corollaries of this formula include Weyl-subconvex bounds for L-functions of weight two cusp forms twisted by quadratic characters, and estimates towards the Ramanujan-Petersson conjecture for Fourier coefficients of weight 3/2 cusp forms.
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