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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.11799 |
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| _version_ | 1866908784836739072 |
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| author | Gilson, Frank |
| author_facet | Gilson, Frank |
| contents | Assuming a mild non-degeneracy condition excluding very low-level Cantor endpoints, and assuming a counting/input hypothesis for the contribution of non-deep orbit indices, we show that for the quadratic field $K=\mathbb{Q}(α)$ there exist constants $A_K,B_K>0$ such that \[ \mathrm{exit}(α)\ \le\ A_K\,(\log_3 H)^2 + B_K. \] Consequently, $\mathrm{dist}(α,\mathcal C)\ge H^{-κ_K\log H}$ for some $κ_K>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11799 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Explicit separation of quadratic irrationals from the middle-third Cantor set Gilson, Frank Number Theory 11J04 Assuming a mild non-degeneracy condition excluding very low-level Cantor endpoints, and assuming a counting/input hypothesis for the contribution of non-deep orbit indices, we show that for the quadratic field $K=\mathbb{Q}(α)$ there exist constants $A_K,B_K>0$ such that \[ \mathrm{exit}(α)\ \le\ A_K\,(\log_3 H)^2 + B_K. \] Consequently, $\mathrm{dist}(α,\mathcal C)\ge H^{-κ_K\log H}$ for some $κ_K>0$. |
| title | Explicit separation of quadratic irrationals from the middle-third Cantor set |
| topic | Number Theory 11J04 |
| url | https://arxiv.org/abs/2601.11799 |