New dimension bounds for \(\alpha \beta\) sets

DOI10.1016/j.jnt.2021.04.018zbMath1485.11109arXiv2102.05979OpenAlexW3169460365WikidataQ114156994 ScholiaQ114156994MaRDI QIDQ2043471

Yanyan Li

Publication date: 2 August 2021

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.05979

zbMATH Keywords

Diophantine approximationself-similar sets\( \alpha \beta\) sets

Mathematics Subject Classification ID

Fractals (28A80) General theory of distribution modulo (1) (11K06) Homogeneous approximation to one number (11J04)

Cites Work

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• Affine embeddings and intersections of Cantor sets
• Multi-rotations on the unit circle
• On \(\alpha\beta\)-sets
• Affine embeddings of Cantor sets on the line
• Affine embeddings of Cantor sets and dimension of \(\alpha\beta\)-sets
• On Furstenberg's intersection conjecture, self-similar measures, and the \(L^q\) norms of convolutions
• Affine embeddings of Cantor sets in the plane
• On uniform distribution of \(\alpha \beta\)-orbits
• A proof of Furstenberg's conjecture on the intersections of \(\times p\)- and \(\times q\)-invariant sets
• Sur un problème de K. Urbanik concernant les ensembles linéaires

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