{"title":"A strengthening of the Bourgain-Kontorovich method: three new theorems","authors":"I. D. Kan","doi":"10.1070/SM9437","DOIUrl":null,"url":null,"abstract":"Consider the set of irreducible denominators of the rational numbers representable by finite continued fractions all of whose partial quotients belong to some finite alphabet . Let the set of infinite continued fractions with partial quotients in this alphabet have Hausdorff dimension satisfying . Then contains a positive share of positive integers. A previous similar result of the author of 2017 was related to the inequality 0.7807\\dots$?> ; in the original 2011 Bourgain-Kontorovich paper, 0.9839\\dots$?> . Bibliography: 28 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sbornik Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/SM9437","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
Consider the set of irreducible denominators of the rational numbers representable by finite continued fractions all of whose partial quotients belong to some finite alphabet . Let the set of infinite continued fractions with partial quotients in this alphabet have Hausdorff dimension satisfying . Then contains a positive share of positive integers. A previous similar result of the author of 2017 was related to the inequality 0.7807\dots$?> ; in the original 2011 Bourgain-Kontorovich paper, 0.9839\dots$?> . Bibliography: 28 titles.
期刊介绍：
The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in:
Mathematical analysis
Ordinary differential equations
Partial differential equations
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Geometry
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Functional analysis
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