Visiting early at prime times
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909293088866304 |
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| author | Haddad, Tony Leung, Sun-Kai Sabuncu, Cihan |
| author_facet | Haddad, Tony Leung, Sun-Kai Sabuncu, Cihan |
| contents | Given an integer $m \geq 2$ and a sufficiently large $q$, we apply a variant of the Maynard--Tao sieve weight to establish the existence of an arithmetic progression with common difference $q$ for which the $m$-th least prime in such progression is $\ll_m q$, which is best possible. As we vary over progressions instead of fixing a particular one, the nature of our result differs from others in the literature. Furthermore, we generalize our result to dynamical systems. The quality of the result depends crucially on the first return time, which we illustrate in the case of Diophantine approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Visiting early at prime times Haddad, Tony Leung, Sun-Kai Sabuncu, Cihan Number Theory Dynamical Systems 11N13, 37A44 Given an integer $m \geq 2$ and a sufficiently large $q$, we apply a variant of the Maynard--Tao sieve weight to establish the existence of an arithmetic progression with common difference $q$ for which the $m$-th least prime in such progression is $\ll_m q$, which is best possible. As we vary over progressions instead of fixing a particular one, the nature of our result differs from others in the literature. Furthermore, we generalize our result to dynamical systems. The quality of the result depends crucially on the first return time, which we illustrate in the case of Diophantine approximation. |
| title | Visiting early at prime times |
| topic | Number Theory Dynamical Systems 11N13, 37A44 |
| url | https://arxiv.org/abs/2408.11781 |