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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Keywords: Lüroth expansion, Hausdorff dimension, relative growth rate
Xiaoyan Tan 1; Zhenliang Zhang 2
@article{CRMATH_2020__358_5_557_0, 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}, }
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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