The relative growth rate for the digits in Lüroth expansions

Xiaoyan Tan; Zhenliang Zhang

doi:10.5802/crmath.71

Théorie « élémentaire » des nombres

The relative growth rate for the digits in Lüroth expansions

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

Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 557-562.

Résumé

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 : 2020-01-08
Révisé le : 2020-04-27
Accepté le : 2020-05-08
Publié le : 2020-09-14

DOI : 10.5802/crmath.71

Classification : 11K55, 28A80
Mots clés : Lüroth expansion, Hausdorff dimension, relative growth rate

Affiliations des auteurs :

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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     author = {Xiaoyan Tan and Zhenliang Zhang},
     title = {The relative growth rate for the digits in {L\"uroth} expansions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {557--562},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {5},
     year = {2020},
     doi = {10.5802/crmath.71},
     language = {en},
}

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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/

Bibliographie
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