The distribution of rational numbers on Cantor's middle thirds set

DOI10.2478/udt-2020-0011zbMath1490.11081arXiv1909.01198OpenAlexW3119782969WikidataQ114041267 ScholiaQ114041267MaRDI QIDQ2129353

Noam Solomon, Barak Weiss, Alexander D. Rahm, Tara Trauthwein

Publication date: 22 April 2022

Published in: Uniform Distribution Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.01198

zbMATH Keywords

fractalprobabilistic modelrational numbers in the Cantor set

Mathematics Subject Classification ID

Metric theory (11J83) Diophantine approximation in probabilistic number theory (11K60)

Related Items (2)

Rational numbers in ×𝑏-invariant sets ⋮ Mahler's question for intrinsic Diophantine approximation on triadic Cantor set: the divergence theory

Cites Work

• Intrinsic approximation on Cantor-like sets, a problem of Mahler
• Schmidt's game on fractals
• On a problem of K. Mahler: Diophantine approximation and Cantor sets
• Diophantine approximation and Cantor sets
• Random walks on homogeneous spaces and Diophantine approximation on fractals
• On the sum \(\sum_{d\mid 2^n-1} d^{-1}\)
• Almost no points on a Cantor set are very well approximable
• Intrinsic approximation for fractals defined by rational iterated function systems: Mahler's research suggestion
• Some suggestions for further research
• Artin's Primitive Root Conjecture – A Survey
• On intrinsic and extrinsic rational approximation to Cantor sets

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