Diophantine approximation with prime denominator in quadratic number fields under GRH
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914893351878656 |
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| author | Baier, Stephan Das, Sourav Molla, Esrafil Ali |
| author_facet | Baier, Stephan Das, Sourav Molla, Esrafil Ali |
| contents | Matomäki proved that if $α\in \mathbb{R}$ is irrational, then there are infinitely many primes $p$ such that $|α-a/p|\le p^{-4/3+\varepsilon}$ for a suitable integer a. In this paper, we extend this result to all quadratic number fields under the condition that the Grand Riemann Hypothesis holds for their Hecke $L$-functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_02628 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Diophantine approximation with prime denominator in quadratic number fields under GRH Baier, Stephan Das, Sourav Molla, Esrafil Ali Number Theory 11J71, 11R11, 11R42, 11R44 Matomäki proved that if $α\in \mathbb{R}$ is irrational, then there are infinitely many primes $p$ such that $|α-a/p|\le p^{-4/3+\varepsilon}$ for a suitable integer a. In this paper, we extend this result to all quadratic number fields under the condition that the Grand Riemann Hypothesis holds for their Hecke $L$-functions. |
| title | Diophantine approximation with prime denominator in quadratic number fields under GRH |
| topic | Number Theory 11J71, 11R11, 11R42, 11R44 |
| url | https://arxiv.org/abs/2312.02628 |