Comptes Rendus
“Elementary” Number Theory
The relative growth rate for the digits in Lüroth expansions
Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 557-562.

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.

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Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.71
Classification: 11K55, 28A80
Keywords: Lüroth expansion, Hausdorff dimension, relative growth rate

Xiaoyan Tan 1; Zhenliang Zhang 2

1 School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, 453003, P. R. China
2 School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401131, P. R.China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Xiaoyan Tan; Zhenliang Zhang. The relative growth rate for the digits in Lüroth expansions. Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 557-562. doi : 10.5802/crmath.71. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.71/

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