On rates of convergence in central limit theorems of Selberg and Bourgade
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912804834902016 |
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| 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 |