{"title":"A Note on the Continued Fraction of Minkowski","authors":"H. Jager","doi":"10.1515/udt-2017-0019","DOIUrl":null,"url":null,"abstract":"Abstract Denote by Θ1,Θ2, · · · the sequence of approximation coefficients of Minkowski’s diagonal continued fraction expansion of a real irrational number x. For almost all x this is a uniformly distributed sequence in the interval [0, 1/2 ]. The average distance between two consecutive terms of this sequence and their correlation coefficient are explicitly calculated and it is shown why these two values are close to 1/6 and 0, respectively, the corresponding values for a random sequence in [0, 1/2].","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"6 1","pages":"125 - 130"},"PeriodicalIF":0.0000,"publicationDate":"2017-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Uniform distribution theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/udt-2017-0019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract Denote by Θ1,Θ2, · · · the sequence of approximation coefficients of Minkowski’s diagonal continued fraction expansion of a real irrational number x. For almost all x this is a uniformly distributed sequence in the interval [0, 1/2 ]. The average distance between two consecutive terms of this sequence and their correlation coefficient are explicitly calculated and it is shown why these two values are close to 1/6 and 0, respectively, the corresponding values for a random sequence in [0, 1/2].
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
