报告题目 (Title)：Sums of Fourier coefficients of automorphic forms（自守形式傅里叶系数的和）

报告人 (Speaker)： 林永晓 教授（山东大学）

报告时间 (Time)：2023年10月8日(周日) 8:45--11:15

报告地点 (Place)：腾讯会议840126000（密码123456）

邀请人(Inviter)：王玉超

主办部门：理学院数学系

报告摘要：The Dirichlet divisor problem asks how precise one can evaluate the partial sum of the divisor function $\tau(n)$, the number of positive divisors of the integer $n$. More generally for $\lambda_F(n)$ given by the Fourier coefficients of an automorphic form $F$ on $\rm{GL}_d$, we will discuss the problem of analyzing sums of $\lambda_F(n)$ weighted by oscillatory exponential functions and their application in bounding partial sum of the coefficients $\lambda_F(n)$. We will discuss several examples where factorization of the coefficients allows some improvements over previous works.