On rates of convergence in central limit theorems of Selberg and Bourgade

Fuente: arXiv
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Main Authors: Hsu, Po-Han, Wong, Peng-Jie
Format: Preprint
Published: 2026
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_version_ 1866912804834902016
author Hsu, Po-Han
Wong, Peng-Jie
author_facet Hsu, Po-Han
Wong, Peng-Jie
contents Based on the recent works of Radziwill-Soundararajan and Roberts, we establish a rate of convergence in Bourgade's central limit theorem for shifted Dirichlet $L$-functions. Our results also indicate that the dependence structure in the components of a random vector could have a dramatic impact on the rate of convergence in such a multivariate central limit theorem.
format Preprint
id arxiv_https___arxiv_org_abs_2601_02781
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On rates of convergence in central limit theorems of Selberg and Bourgade
Hsu, Po-Han
Wong, Peng-Jie
Number Theory
Probability
Primary 11M06, Secondary 11M41, 60F05
Based on the recent works of Radziwill-Soundararajan and Roberts, we establish a rate of convergence in Bourgade's central limit theorem for shifted Dirichlet $L$-functions. Our results also indicate that the dependence structure in the components of a random vector could have a dramatic impact on the rate of convergence in such a multivariate central limit theorem.
title On rates of convergence in central limit theorems of Selberg and Bourgade
topic Number Theory
Probability
Primary 11M06, Secondary 11M41, 60F05
url https://arxiv.org/abs/2601.02781