{"title":"Mahler’s Conjecture on ξ(3/2)nmod 1","authors":"O. Strauch","doi":"10.2478/udt-2021-0007","DOIUrl":null,"url":null,"abstract":"Abstract K. Mahler’s conjecture: There exists no ξ ∈ ℝ+ such that the fractional parts {ξ(3/2)n} satisfy 0 ≤ {ξ(3/2)n} < 1/2 for all n = 0, 1, 2,... Such a ξ, if exists, is called a Mahler’s Z-number. In this paper we prove that if ξ is a Z-number, then the sequence xn = {ξ(3/2)n}, n =1, 2,... has asymptotic distribution function c0(x), where c0(x)=1 for x ∈ (0, 1].","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"410 1","pages":"49 - 70"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Uniform distribution theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/udt-2021-0007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract K. Mahler’s conjecture: There exists no ξ ∈ ℝ+ such that the fractional parts {ξ(3/2)n} satisfy 0 ≤ {ξ(3/2)n} < 1/2 for all n = 0, 1, 2,... Such a ξ, if exists, is called a Mahler’s Z-number. In this paper we prove that if ξ is a Z-number, then the sequence xn = {ξ(3/2)n}, n =1, 2,... has asymptotic distribution function c0(x), where c0(x)=1 for x ∈ (0, 1].
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