Intrinsic Diophantine approximation by rationals of height with a bounded number of distinct prime factors

Edouard Daviaud

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arXiv · 2602.02379

Intrinsic Diophantine approximation by rationals of height with a bounded number of distinct prime factors

Edouard Daviaud

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Abstract

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 $\psi$-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.

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Edouard Daviaud. 2026-02-02. Intrinsic Diophantine approximation by rationals of height with a bounded number of distinct prime factors. https://arxiv.org/abs/2602.02379

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