On rates of convergence in central limit theorems of Selberg and Bourgade
Abstract
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.
Fields of Study & Subjects
Random Matrices and Applications
Probability and Risk Models
Bayesian Methods and Mixture Models
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 6 January 2026
- Document type
- Preprint