Diophantine Approximation with Piatetski-Shapiro Primes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918140154216448 |
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| author | Baier, Stephan Rahaman, Habibur |
| author_facet | Baier, Stephan Rahaman, Habibur |
| contents | We prove that for every irrational number $α$, real number $β$, real number $c$ satisfying $1<c<9/8$ and positive real number $θ$ satisfying $θ<(9/c-8)/10$, there exist infinitely many primes of the form $p=\left[n^c\right]$ with $n\in \mathbb{N}$ such that $||αp||<p^{-θ}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diophantine Approximation with Piatetski-Shapiro Primes Baier, Stephan Rahaman, Habibur Number Theory 11J25, 11J54, 11J71, 11L07, 11L20, 11N36 We prove that for every irrational number $α$, real number $β$, real number $c$ satisfying $1<c<9/8$ and positive real number $θ$ satisfying $θ<(9/c-8)/10$, there exist infinitely many primes of the form $p=\left[n^c\right]$ with $n\in \mathbb{N}$ such that $||αp||<p^{-θ}$. |
| title | Diophantine Approximation with Piatetski-Shapiro Primes |
| topic | Number Theory 11J25, 11J54, 11J71, 11L07, 11L20, 11N36 |
| url | https://arxiv.org/abs/2408.01314 |