{"title":"An improved convergence case for Diophantine approximations on IFS fractals","authors":"Itamar Cohen-Matalon","doi":"10.2140/moscow.2023.12.97","DOIUrl":null,"url":null,"abstract":"The objective of this paper is to (partially) address the issue of finding an analogue to Khintchine's theorem for IFS Fractals. We study the convergence case for Diophantine approximations, and show an improved result for higher dimensions. This matter has been previously studied by Pollington and Velani in arXiv:math/0401149. Pollington and Velani show a similar result to the one in this paper (a Khinchine convergence case) and we shall show how our result is an improvement in the higher dimensional cases.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow Journal of Combinatorics and Number Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/moscow.2023.12.97","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
The objective of this paper is to (partially) address the issue of finding an analogue to Khintchine's theorem for IFS Fractals. We study the convergence case for Diophantine approximations, and show an improved result for higher dimensions. This matter has been previously studied by Pollington and Velani in arXiv:math/0401149. Pollington and Velani show a similar result to the one in this paper (a Khinchine convergence case) and we shall show how our result is an improvement in the higher dimensional cases.
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