Speaker:Liu Shenhui, the Ohio State University, USA

Date:December 15, 2016

Time:2:00 pm--3:00 pm

Location:B1044

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:

http://www.maths.sdu.edu.cn/the-first-moment-of-symmetric-square-l-functions-in-the-weight-aspect.html

Edited by: Liu Huan