»ã±¨±êÌâ (Title)£ºSums of Fourier coefficients of automorphic forms£¨×ÔÊØ´ó¾Ö¸Â·ïҶϵÊýµÄºÍ£©

»ã±¨ÈË (Speaker)£º ÁÖÓÀÏþ ½ÌÊÚ£¨É½¶«´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê10ÔÂ8ÈÕ(ÖÜÈÕ) 8:45--11:15

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒé840126000£¨ÃÜÂë123456£©

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»ã±¨ÌáÒª£ºThe 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.