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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2404.15123 |
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| _version_ | 1866913326133411840 |
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| author | Hauke, Manuel Saez, Santiago Vazquez Walker, Aled |
| author_facet | Hauke, Manuel Saez, Santiago Vazquez Walker, Aled |
| contents | We present a novel proof of the Duffin-Schaeffer conjecture in metric Diophantine approximation. Our proof is heavily motivated by the ideas of Koukoulopoulos-Maynard's breakthrough first argument, but simplifies and strengthens several technical aspects. In particular, we avoid any direct handling of GCD graphs and their `quality'. We also consider the metric quantitative theory of Diophantine approximations, improving the $(\log Ψ(N))^{-C}$ error-term of Aistleitner-Borda and the first named author to $\exp(-(\log Ψ(N))^{\frac{1}{2} - \varepsilon})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15123 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proving the Duffin-Schaeffer conjecture without GCD graphs Hauke, Manuel Saez, Santiago Vazquez Walker, Aled Number Theory We present a novel proof of the Duffin-Schaeffer conjecture in metric Diophantine approximation. Our proof is heavily motivated by the ideas of Koukoulopoulos-Maynard's breakthrough first argument, but simplifies and strengthens several technical aspects. In particular, we avoid any direct handling of GCD graphs and their `quality'. We also consider the metric quantitative theory of Diophantine approximations, improving the $(\log Ψ(N))^{-C}$ error-term of Aistleitner-Borda and the first named author to $\exp(-(\log Ψ(N))^{\frac{1}{2} - \varepsilon})$. |
| title | Proving the Duffin-Schaeffer conjecture without GCD graphs |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.15123 |