[Quelques propriétés de lacunarité des quotients partiels de nombres réels]
Nous considérons des propriétés de lacunarité de la suite des quotients partiels du développement en fraction continue de nombres réels. Nous calculons la dimension de Hausdorff d’ensembles de points dont la suite des quotients partiels satisfait à différentes conditions de lacunarité.
We consider lacunarity properties of sequence of partial quotients for real numbers in their continued fraction expansions. Hausdorff dimension of the sets of points with different lacunarity conditions on their partial quotients are calculated.
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Keywords: Hausdorff dimension, Continued fraction expansion.
Mot clés : Dimension de Hausdorff, développement en fraction continue.
Xuan Zhao 1 ; Zhenliang Zhang 2
CC-BY 4.0
@article{CRMATH_2024__362_G10_1089_0,
author = {Xuan Zhao and Zhenliang Zhang},
title = {Some lacunarity properties of partial quotients of real numbers},
journal = {Comptes Rendus. Math\'ematique},
pages = {1089--1095},
publisher = {Acad\'emie des sciences, Paris},
volume = {362},
year = {2024},
doi = {10.5802/crmath.594},
language = {en},
}
Xuan Zhao; Zhenliang Zhang. Some lacunarity properties of partial quotients of real numbers. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1089-1095. doi : 10.5802/crmath.594. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.594/
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