An explicit version of Bombieri's log-free density estimate and Sárközy's theorem for shifted primes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912176871047168 |
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| author | Thorner, Jesse Zaman, Asif |
| author_facet | Thorner, Jesse Zaman, Asif |
| contents | We make explicit Bombieri's refinement of Gallagher's log-free "large sieve density estimate near $σ= 1$" for Dirichlet $L$-functions. We use this estimate and recent work of Green to prove that if $N\geq 2$ is an integer, $A\subseteq\{1,\ldots,N\}$, and for all primes $p$ no two elements in $A$ differ by $p-1$, then $|A|\ll N^{1-1/10^{18}}$. This strengthens a theorem of Sárközy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_11123 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An explicit version of Bombieri's log-free density estimate and Sárközy's theorem for shifted primes Thorner, Jesse Zaman, Asif Number Theory We make explicit Bombieri's refinement of Gallagher's log-free "large sieve density estimate near $σ= 1$" for Dirichlet $L$-functions. We use this estimate and recent work of Green to prove that if $N\geq 2$ is an integer, $A\subseteq\{1,\ldots,N\}$, and for all primes $p$ no two elements in $A$ differ by $p-1$, then $|A|\ll N^{1-1/10^{18}}$. This strengthens a theorem of Sárközy. |
| title | An explicit version of Bombieri's log-free density estimate and Sárközy's theorem for shifted primes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2208.11123 |