Intrinsic Diophantine approximation by rationals of height with a bounded number of distinct prime factors
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 $ψ$-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.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Analytic Number Theory Research
advanced mathematical theories
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 2 February 2026
- Document type
- Preprint