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| Main Author: | |
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| Format: | Preprint |
| Published: |
2012
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1203.1759 |
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| _version_ | 1866909428547059712 |
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| author | Ramaré, Olivier |
| author_facet | Ramaré, Olivier |
| contents | We prove non-trivial lower bounds for sums of type $\sum_{p\sim P}g(γ\Log p)$, where $g$ is a non-negative $2π$-periodical function and $γ$ is a given parameter. As an application we prove that $ζ(1+it)^{\pm1}\ll\Log\Log (9+|t|)$ and extend the zero-free region of the Riemann zeta-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1203_1759 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | On the behaviour of $γ\Log p$ modulo 1 Ramaré, Olivier Number Theory We prove non-trivial lower bounds for sums of type $\sum_{p\sim P}g(γ\Log p)$, where $g$ is a non-negative $2π$-periodical function and $γ$ is a given parameter. As an application we prove that $ζ(1+it)^{\pm1}\ll\Log\Log (9+|t|)$ and extend the zero-free region of the Riemann zeta-function. |
| title | On the behaviour of $γ\Log p$ modulo 1 |
| topic | Number Theory |
| url | https://arxiv.org/abs/1203.1759 |