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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.17544 |
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| _version_ | 1866914848704561152 |
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| author | Gambini, Alessandro |
| author_facet | Gambini, Alessandro |
| contents | Let $1<k<7/6$, $λ_1,λ_2,λ_3$ and $λ_4$ be non-zero real numbers, not all of the same sign such that $λ_1/λ_2$ is irrational and let $ω$ be a real number. We prove that the inequality $|λ_1p_1^2+λ_2p_2^2+λ_3p_3^2+λ_4p_4^k-ω|\le (\max_j p_j)^{-\frac{7-6k}{14k}+\varepsilon}$ has infinitely many solutions in prime variables $p_1,p_2,p_3,p_4$ for any $\varepsilon>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diophantine approximation with a quaternary problem Gambini, Alessandro Number Theory Let $1<k<7/6$, $λ_1,λ_2,λ_3$ and $λ_4$ be non-zero real numbers, not all of the same sign such that $λ_1/λ_2$ is irrational and let $ω$ be a real number. We prove that the inequality $|λ_1p_1^2+λ_2p_2^2+λ_3p_3^2+λ_4p_4^k-ω|\le (\max_j p_j)^{-\frac{7-6k}{14k}+\varepsilon}$ has infinitely many solutions in prime variables $p_1,p_2,p_3,p_4$ for any $\varepsilon>0$. |
| title | Diophantine approximation with a quaternary problem |
| topic | Number Theory |
| url | https://arxiv.org/abs/2406.17544 |