Speaker:刘慎徽      The Ohio State University

Venue:B1044

Time:2016年12月15日 14:00-15:00

Title:The first moment of symmetric square L-functions in the weight aspect

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.