Intrinsic Diophantine approximation by rationals of height with a bounded number of distinct prime factors
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915858400411648 |
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| author | Daviaud, Edouard |
| author_facet | Daviaud, Edouard |
| contents | In this article, for a large class of rational self-similar IFS's wich contains the middle-third Cantor set, we compute the Hausdorff dimension of elements a self-similar set that are $ψ$-approximable by rational belonging to this set and satisfying that its numerator has a bounded number of distinct prime divisors. This paper is based on a previous version in which the proof of a lemma (Lemma 3.8) was incorrect. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02379 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Intrinsic Diophantine approximation by rationals of height with a bounded number of distinct prime factors Daviaud, Edouard Number Theory In this article, for a large class of rational self-similar IFS's wich contains the middle-third Cantor set, we compute the Hausdorff dimension of elements a self-similar set that are $ψ$-approximable by rational belonging to this set and satisfying that its numerator has a bounded number of distinct prime divisors. This paper is based on a previous version in which the proof of a lemma (Lemma 3.8) was incorrect. |
| title | Intrinsic Diophantine approximation by rationals of height with a bounded number of distinct prime factors |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.02379 |