THE MULTIVARIATE RATE OF CONVERGENCE FOR SELBERG'S CENTRAL LIMIT THEOREM

• 成果类型: Article
• 署名作者: Roberts, Asher
• 署名单位: City University of New York (CUNY) System
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2042
• 发表日期: 2024
• 页码: 3348-3369
• 关键词: mod-gaussian convergence; matrix

摘要

In this paper we quantify the rate of convergence in Selberg's central limit theorem for log |zeta (1/2 + it)| based on the method of proof given by the same rate of convergence of (log log log T )2/root log log T as Selberg in (In 1989) Univ (1992) 367-385) in the Kolmogorov distance by using the Dudley distance instead. We also prove the theorem for the multivariate case given by same rate of convergence as in the single variable case.