Resonance sums for Rankin-Selberg L-functions

Speaker: Yangbo Ye (The University of Iowa)

Venue: B924

Time: June 29th, 10:30-11:30

Title: Resonance sums for Rankin-Selberg L-functions

Abstract: Let f and g be Maass cusp forms for SL(m,Z) and SL(k,Z), respectively. Denote by a(n) the Fourier coefficient of the Rankin-Selberg L-function L(s,fxg). Kyle Czarnecki proved an asymptotic formula for a Voronoi-type formula for a(n). As an application he estimated a smooth sum of a(n) against e(c n^b) and discovered that the resonance occurs when b=1/(mk) and |c| is near mk q^(1/mk) for a positive integer q. This result provides an evidence that the Rankin-Selberg product fxg is automorphic.