On the $b$-ary expansion of a real number whose irrationality exponent is close to 2
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910144737050624 |
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| author | Bugeaud, Yann Kim, Dong Han |
| author_facet | Bugeaud, Yann Kim, Dong Han |
| contents | Let $b \ge 2$ be an integer and $ξ$ an irrational real number. We establishes that, if the irrationality exponent of $ξ$ is less than $2.324 \ldots$, then the $b$-ary expansion of $ξ$ cannot be `too simple', in a suitable sense. This improves the results of our previous paper [Ann. Sc. Norm. Super. Pisa Cl. Sci., 2017]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_02059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the $b$-ary expansion of a real number whose irrationality exponent is close to 2 Bugeaud, Yann Kim, Dong Han Number Theory 11A63, 11J82, 68R15 Let $b \ge 2$ be an integer and $ξ$ an irrational real number. We establishes that, if the irrationality exponent of $ξ$ is less than $2.324 \ldots$, then the $b$-ary expansion of $ξ$ cannot be `too simple', in a suitable sense. This improves the results of our previous paper [Ann. Sc. Norm. Super. Pisa Cl. Sci., 2017]. |
| title | On the $b$-ary expansion of a real number whose irrationality exponent is close to 2 |
| topic | Number Theory 11A63, 11J82, 68R15 |
| url | https://arxiv.org/abs/2510.02059 |