Speaker: Liu Shenhui, the Ohio State University, USA
Date: December 15, 2016
Time: 2:00 pm--3:00 pm
Sponsor: the School of Mathematics
Abstract: We will talk about the average behavior of symmetric square L-functions at 1/2 for classical modular forms in the weight aspect. Specifically, we present an asymptotic formula for the first moment of L(1/2,sym^2f) with arbitrary power saving, where f ranges over a Hecke basis of weight-k cusp forms for the full modular group. The approach taken allows us to extract two secondary main terms from the best known error term. And these secondary main terms exhibit a connection between the symmetric square L-functions and quadratic fields, which is the main theme of Zagier’s work Modular forms whose coefficients involve zeta-functions of quadratic fields in 1977.
For more information, please visit:
Edited by: Liu Huan