The relative growth rate for the digits in Lüroth expansions

descriptionPublicationkeyboard_double_arrow_right Article 14 Sep 2020 English Publisher:MathDoc/Centre MersenneJournal:Comptes Rendus. Mathématique, volume 358, pages 557-562 (issn: 1631-073X, eissn: 1778-3569,

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Authors: Tan, Xiaoyan; Zhang, Zhenliang;

doi: 10.5802/crmath.71

The relative growth rate for the digits in Lüroth expansions

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Abstract

In this note, the rate of growth of digits in the Lüroth expansion of an irrational number is studied relative to the rate of approximation of the number by its convergents. The Hausdorff dimension of exceptional sets of points with a given relative growth rate is established.

Related Organizations

Chongqing Normal University
China (People's Republic of)
Henan Institute of Science and Technology
China (People's Republic of)

Keywords

Fractals, Lüroth expansion, relative growth rate, QA1-939, Metric theory of other algorithms and expansions; measure and Hausdorff dimension, Hausdorff dimension, Mathematics

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