论文标题
Selberg的中央限制定理的多元收敛速率
The Multivariate Rate of Convergence for Selberg's Central Limit Theorem
论文作者
论文摘要
在本文中，我们基于Radziwill和Soundararajan给出的证明方法来量化Selberg的中心限制定理中的收敛速率（1/2+IT）| $。我们实现了$（\ log \ log \ log t）^2/\ sqrt {\ log \ log t} $与selberg在Kolmogorov距离中使用Dudley距离相同的收敛速率。我们还证明了Bourgade给出的多元案例定理，其收敛速度与单个变量情况相同。
In this paper we quantify the rate of convergence in Selberg's central limit theorem for $\log|ζ(1/2+it)|$ based on the method of proof given by Radziwill and Soundararajan. We achieve the same rate of convergence of $(\log\log\log T)^2/\sqrt{\log\log T}$ as Selberg in the Kolmogorov distance by using the Dudley distance instead. We also prove the theorem for the multivariate case given by Bourgade with the same rate of convergence as in the single variable case.
