A strengthening of the Bourgain-Kontorovich method: three new theorems

IF 0.8 4区数学 Q2 MATHEMATICS

Sbornik Mathematics Pub Date : 2021-01-01 DOI:10.1070/SM9437

I. D. Kan

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.

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bourgin - kontorovich方法的强化:三个新定理

考虑可由有限连分式表示的有理数的不可约分母的集合，所有这些有理数的部分商都属于某个有限字母。设该字母表中具有部分商的无限连分式集合具有满足的豪斯多夫维数。则包含正整数的正份额。作者在2017年的一个类似结果与不等式0.7807\dots$?>;在2011年的Bourgain-Kontorovich论文中，0.9839\dots$?>。参考书目:28种。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

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 Mathematical physics Geometry Algebra Functional analysis