{"title":"Rational approximations to two irrational numbers","authors":"N. Shulga","doi":"10.2140/moscow.2022.11.1","DOIUrl":null,"url":null,"abstract":"For real ξ we consider the irrationality measure function ψξ(t) = min16q6t,q∈Z ||qξ||. We prove that in the case α± β / ∈ Z there exist arbitrary large values of t with ∣ ∣ ∣ 1 ψα(t) − 1 ψβ(t) ∣ ∣ ∣> √ 5 ","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow Journal of Combinatorics and Number Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/moscow.2022.11.1","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: 2
Abstract
For real ξ we consider the irrationality measure function ψξ(t) = min16q6t,q∈Z ||qξ||. We prove that in the case α± β / ∈ Z there exist arbitrary large values of t with ∣ ∣ ∣ 1 ψα(t) − 1 ψβ(t) ∣ ∣ ∣> √ 5
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