On a Theorem of Nathanson on Diophantine Approximation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929422063370240 |
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| author | Hančl, Jaroslav Nguyen, Tho Phuoc |
| author_facet | Hančl, Jaroslav Nguyen, Tho Phuoc |
| contents | In 1974, M. B. Nathanson proved that every irrational number $α$ represented by a simple continued fraction with infinitely many elements greater than or equal to $k$ is approximable by an infinite number of rational numbers $p/q$ satisfying $|α-p/q|<1/(\sqrt{k^2+4}q^2)$. In this paper we refine this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11525 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Theorem of Nathanson on Diophantine Approximation Hančl, Jaroslav Nguyen, Tho Phuoc Number Theory 11J82, 11A55 In 1974, M. B. Nathanson proved that every irrational number $α$ represented by a simple continued fraction with infinitely many elements greater than or equal to $k$ is approximable by an infinite number of rational numbers $p/q$ satisfying $|α-p/q|<1/(\sqrt{k^2+4}q^2)$. In this paper we refine this result. |
| title | On a Theorem of Nathanson on Diophantine Approximation |
| topic | Number Theory 11J82, 11A55 |
| url | https://arxiv.org/abs/2407.11525 |