Lüroth Expansions in Diophantine Approximation: Metric Properties and Conjectures

Fuente: arXiv
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Auteur principal: Lee, Ying Wai
Format: Preprint
Publié: 2025
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author Lee, Ying Wai
author_facet Lee, Ying Wai
contents This paper focuses on the metric properties of Lüroth well approximable numbers, studying analogous of classical results, namely the Khintchine Theorem, the Jarník--Besicovitch Theorem, and the result of Dodson. A supplementary proof is provided for a measure-theoretic statement originally proposed by Tan--Zhou. The Beresnevich--Velani Mass Transference Principle is applied to extend a dimensional result of Cao--Wu--Zhang. A counterexample is constructed, leading to a revision of a conjecture by Tan--Zhou concerning dimension, along with a partial result.
format Preprint
id arxiv_https___arxiv_org_abs_2502_08408
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Lüroth Expansions in Diophantine Approximation: Metric Properties and Conjectures
Lee, Ying Wai
Number Theory
This paper focuses on the metric properties of Lüroth well approximable numbers, studying analogous of classical results, namely the Khintchine Theorem, the Jarník--Besicovitch Theorem, and the result of Dodson. A supplementary proof is provided for a measure-theoretic statement originally proposed by Tan--Zhou. The Beresnevich--Velani Mass Transference Principle is applied to extend a dimensional result of Cao--Wu--Zhang. A counterexample is constructed, leading to a revision of a conjecture by Tan--Zhou concerning dimension, along with a partial result.
title Lüroth Expansions in Diophantine Approximation: Metric Properties and Conjectures
topic Number Theory
url https://arxiv.org/abs/2502.08408