THE SHIFTED CONVOLUTION OF DIVISOR FUNCTIONS
THE SHIFTED CONVOLUTION OF DIVISOR FUNCTIONS
复制标题
DOI：
10.1093/qmath/haw010
复制
发表时间：
2015-06
影响因子：
0.7
通讯作者：
Berke Topacogullari
中科院分区：
文献类型：
--
作者：
Berke Topacogullari
本文证明了除数函数d_3（n）和d（n）的移位卷积的一个渐近公式，它在移位参数上是一致的，并且具有一个省电的误差项。该方法也被应用于d_3（n）的移位卷积和全纯尖点形式的Fourier系数的类似估计。这些渐近性改进了几个不同作者以前的结果。
We prove an asymptotic formula for the shifted convolution of the divisor functions $d_3(n)$ and $d(n)$, which is uniform in the shift parameter and which has a power-saving error term. The method is also applied to give analogous estimates for the shifted convolution of $d_3(n)$ and Fourier coefficents of holomorphic cusp forms. These asymptotics improve previous results obtained by several different authors.