On the distribution of $αp$ modulo one over Piatetski-Shapiro primes
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866909598104944640 |
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| author | Dimitrov, S. I. |
| author_facet | Dimitrov, S. I. |
| contents | Let $[\, \cdot\,]$ be the floor function and $\|x\|$ denotes the distance from $x$ to the nearest integer. In this paper we show that whenever $α$ is irrational and $β$ is real then for any fixed $1<c<12/11$ there exist infinitely many prime numbers $p$ satisfying the inequality \begin{equation*} \|αp+β\|\ll p^{\frac{11c-12}{26c}}\log^6p \end{equation*} and such that $p=[n^c]$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2005_05008 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the distribution of $αp$ modulo one over Piatetski-Shapiro primes Dimitrov, S. I. Number Theory Let $[\, \cdot\,]$ be the floor function and $\|x\|$ denotes the distance from $x$ to the nearest integer. In this paper we show that whenever $α$ is irrational and $β$ is real then for any fixed $1<c<12/11$ there exist infinitely many prime numbers $p$ satisfying the inequality \begin{equation*} \|αp+β\|\ll p^{\frac{11c-12}{26c}}\log^6p \end{equation*} and such that $p=[n^c]$. |
| title | On the distribution of $αp$ modulo one over Piatetski-Shapiro primes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2005.05008 |