no. 5
Théorie « élémentaire » des nombres
The relative growth rate for the digits in Lüroth expansions
Tan, Xiaoyan1 ; Zhang, Zhenliang2 
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, Tome 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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Publié le :
DOI : 10.5802/crmath.71
Classification : 11K55, 28A80
Mots clés : Lüroth expansion, Hausdorff dimension, relative growth rate
Tan, Xiaoyan 1 ; Zhang, Zhenliang 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 
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Tan, Xiaoyan; Zhang, Zhenliang. The relative growth rate for the digits in Lüroth expansions. Comptes Rendus. Mathématique, Tome 358 (2020) no. 5, pp. 557-562. doi : 10.5802/crmath.71. http://archive.numdam.org/articles/10.5802/crmath.71/

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