Large deviations for number of irreducible divisors of the Dirichlet series distribution
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918208120815616 |
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| author | Cranston, Michael Khodiakova, Mariia |
| author_facet | Cranston, Michael Khodiakova, Mariia |
| contents | In this paper we produce precise large deviation estimates through the lens of mod-Poisson convergence. We apply a general result to various examples from number theory, Dedekind domains and polynomials over finite fields when an element is selected using a distribution based on a Dirichlet series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large deviations for number of irreducible divisors of the Dirichlet series distribution Cranston, Michael Khodiakova, Mariia Number Theory 11A41, 11R42, 11R59, 60F10 In this paper we produce precise large deviation estimates through the lens of mod-Poisson convergence. We apply a general result to various examples from number theory, Dedekind domains and polynomials over finite fields when an element is selected using a distribution based on a Dirichlet series. |
| title | Large deviations for number of irreducible divisors of the Dirichlet series distribution |
| topic | Number Theory 11A41, 11R42, 11R59, 60F10 |
| url | https://arxiv.org/abs/2511.14234 |