Diophantine approximation with mixed powers of Piatetski-Shapiro primes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915850990125056 |
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| author | Dimitrov, S. I. |
| author_facet | Dimitrov, S. I. |
| contents | Let $[\,\cdot\,]$ denote the floor function. In this paper, we show that whenever $η$ is real and the constants $λ_i$ satisfy some necessary conditions, then for any fixed $\frac{63}{64}<γ<1$ and $θ>0$, there exist infinitely many prime triples $p_1,\, p_2,\, p_3$ satisfying the inequality \begin{equation*} |λ_1p_1 + λ_2p_2 + λ_3p^2_3+η|<\big(\max \{p_1, p_2, p^2_3\}\big)^{{\frac{63-64γ}{52}}+θ} \end{equation*} and such that $p_i=[n_i^{1/γ}]$, $i=1,\,2,\,3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09771 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diophantine approximation with mixed powers of Piatetski-Shapiro primes Dimitrov, S. I. Number Theory Let $[\,\cdot\,]$ denote the floor function. In this paper, we show that whenever $η$ is real and the constants $λ_i$ satisfy some necessary conditions, then for any fixed $\frac{63}{64}<γ<1$ and $θ>0$, there exist infinitely many prime triples $p_1,\, p_2,\, p_3$ satisfying the inequality \begin{equation*} |λ_1p_1 + λ_2p_2 + λ_3p^2_3+η|<\big(\max \{p_1, p_2, p^2_3\}\big)^{{\frac{63-64γ}{52}}+θ} \end{equation*} and such that $p_i=[n_i^{1/γ}]$, $i=1,\,2,\,3$. |
| title | Diophantine approximation with mixed powers of Piatetski-Shapiro primes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2512.09771 |