Lower bounds for the Hausdorff dimension of expressible sets
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866916049410064384 |
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| author | Gravgaard, Maiken Kristensen, Simon Hančl, Jaroslav |
| author_facet | Gravgaard, Maiken Kristensen, Simon Hančl, Jaroslav |
| contents | We obtain positive lower bounds on the Hausdorff dimension of sets of real numbers given by expressions of the form $\sum_{n=1}^\infty \frac{1}{a_n b_n}$, where $b_n$ satisfies some growth condition and $a_n$ lies in some set, possibly depending on $n$. As a consequence of our results, some of the irrational numbers arising from Erdős' celebrated construction from 1976 are not Liouville numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26839 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lower bounds for the Hausdorff dimension of expressible sets Gravgaard, Maiken Kristensen, Simon Hančl, Jaroslav Number Theory 11J83 11K55 We obtain positive lower bounds on the Hausdorff dimension of sets of real numbers given by expressions of the form $\sum_{n=1}^\infty \frac{1}{a_n b_n}$, where $b_n$ satisfies some growth condition and $a_n$ lies in some set, possibly depending on $n$. As a consequence of our results, some of the irrational numbers arising from Erdős' celebrated construction from 1976 are not Liouville numbers. |
| title | Lower bounds for the Hausdorff dimension of expressible sets |
| topic | Number Theory 11J83 11K55 |
| url | https://arxiv.org/abs/2605.26839 |