Rankin-Selberg Without Unfolding and Gelfand Pairs

IAS/PU NUMBER THEORY
Topic:Rankin-Selberg Without Unfolding and Gelfand Pairs
Speaker:A. Reznikov
Affiliation:Bar Ilan University
Date:Thursday, February 8
Time/Room:4:30pm - 5:30pm/Fine Hall 322, Princeton University

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.)