论文标题
在短移动间隔内的典型乘法功能的部分总和
Partial sums of typical multiplicative functions over short moving intervals
论文作者
论文摘要
我们证明，在间隔$（x，x，x+h] $上，$ k $ th的积极整数段落的二次乘以随机乘法功能与相应的高斯时刻相匹配，只要$ h \ ll x/（\ log x/（\ log x）^{2k^2k^2+2+2+2+2+2+o（1）} $和$ h $ typrys fortry plastial norky plastial short plastial short nortial fortial short nortial short plastial short。由随机乘法功能实现产生的乘法功能在短移动间隔中具有高斯限制分布，$（x，x+h] $，$ h \ ll x/（\ log x）^{w（x）^{w（x）} $呈$ x $，$ x $在$ x $中，$ x $从$ x $中均匀地选择了$ \ \ \ \ \ \ \ {1,2，\ d;随着$ x $的任意，这在最近的哈珀问题上取得了一些最初的进展。
We prove that the $k$-th positive integer moment of partial sums of Steinhaus random multiplicative functions over the interval $(x, x+H]$ matches the corresponding Gaussian moment, as long as $H\ll x/(\log x)^{2k^2+2+o(1)}$ and $H$ tends to infinity with $x$. We show that properly normalized partial sums of typical multiplicative functions arising from realizations of random multiplicative functions have Gaussian limiting distribution in short moving intervals $(x, x+H]$ with $H\ll X/(\log X)^{W(X)}$ tending to infinity with $X$, where $x$ is uniformly chosen from $\{1,2,\dots, X\}$, and $W(X)$ tends to infinity with $X$ arbitrarily slowly. This makes some initial progress on a recent question of Harper.
