Joint IAS/Princeton University Number Theory Seminar

I describe a new simple way to obtain Rankin-Selberg type spectral identities. These include the classical Rankin-Selberg identity, the Motohashi identity for the forth moment of the zeta function and many new identities between various L-functions. I discuss an analytic application of some of these identities towards nontrivial bounds for various Fourier coefficients of cusp forms. (Joint work with J. Bernstein.)