bourgin - kontorovich方法的强化:三个新定理

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

I. D. Kan

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引用次数: 4

摘要

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。

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

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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