On the distribution of $αp^2$ modulo one over primes of the form $[n^c]$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908382577819648 |
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| author | Dimitrov, S. I. Lazarova, M. D. |
| author_facet | Dimitrov, S. I. Lazarova, M. D. |
| contents | Let $[\, \cdot\,]$ be the floor function and $\|x\|$ denote 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 $\frac{13}{14}<γ<1$, there exist infinitely many prime numbers $p$ satisfying the inequality \begin{equation*} \|αp^2+β\|< p^{\frac{13-14γ}{29}+\varepsilon} \end{equation*} and such that $p=[n^{1/γ}]$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_21333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the distribution of $αp^2$ modulo one over primes of the form $[n^c]$ Dimitrov, S. I. Lazarova, M. D. Number Theory Let $[\, \cdot\,]$ be the floor function and $\|x\|$ denote 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 $\frac{13}{14}<γ<1$, there exist infinitely many prime numbers $p$ satisfying the inequality \begin{equation*} \|αp^2+β\|< p^{\frac{13-14γ}{29}+\varepsilon} \end{equation*} and such that $p=[n^{1/γ}]$. |
| title | On the distribution of $αp^2$ modulo one over primes of the form $[n^c]$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.21333 |