Comptes Rendus
no. 5
Théorie « élémentaire » des nombres
The relative growth rate for the digits in Lüroth expansions
Xiaoyan Tan1 ; Zhenliang Zhang2 
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
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.

Reçu le :
Révisé le :
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DOI : 10.5802/crmath.71
Classification : 11K55, 28A80
Mots clés : 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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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