Some lacunarity properties of partial quotients of real numbers
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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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.594/ |
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| author | Zhao, Xuan Zhang, Zhenliang |
| author_facet | Zhao, Xuan Zhang, Zhenliang |
| author_sort | Zhao, Xuan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-abd5e566ea3145cd832100ce5aff1376 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-abd5e566ea3145cd832100ce5aff13762025-02-07T11:23:31ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G101089109510.5802/crmath.59410.5802/crmath.594Some lacunarity properties of partial quotients of real numbersZhao, Xuan0Zhang, Zhenliang1National Education Examinations Authority, 100084 Beijing, ChinaSchool of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, P. R. ChinaWe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.594/Hausdorff dimensionContinued fraction expansion. |
| spellingShingle | Zhao, Xuan Zhang, Zhenliang Some lacunarity properties of partial quotients of real numbers Comptes Rendus. Mathématique Hausdorff dimension Continued fraction expansion. |
| title | Some lacunarity properties of partial quotients of real numbers |
| title_full | Some lacunarity properties of partial quotients of real numbers |
| title_fullStr | Some lacunarity properties of partial quotients of real numbers |
| title_full_unstemmed | Some lacunarity properties of partial quotients of real numbers |
| title_short | Some lacunarity properties of partial quotients of real numbers |
| title_sort | some lacunarity properties of partial quotients of real numbers |
| topic | Hausdorff dimension Continued fraction expansion. |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.594/ |
| work_keys_str_mv | AT zhaoxuan somelacunaritypropertiesofpartialquotientsofrealnumbers AT zhangzhenliang somelacunaritypropertiesofpartialquotientsofrealnumbers |