Lecture on "the First Moment of Symmetric Square L-functions in the Weight Aspect"
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Lecture on "the First Moment of Symmetric Square L-functions in the Weight Aspect"
DateandTime: 2016-12-15 21:27:25

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




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