比较正则连分式和后向连分式：lochs型定理和近似性质

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-10-01 DOI:10.1016/j.jnt.2025.09.006

Zhigang Tian , Lulu Fang

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引用次数: 0

摘要

本文研究了正则连分式与倒连分式之间的两个关系问题。第一个问题解决了rcf和BCFs的lochs型定理，其中我们将一个展开式中的部分商的数量作为另一个展开式中部分商数量的函数进行比较。第二个问题研究了rcf和BCFs的近似性质，特别注意了bcf比rcf更能无限近似无理数的集合。证明了该集合具有勒贝格测度零，并进一步从贝尔范畴和分形维数的角度对其进行了分析。

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Comparing regular and backward continued fractions: Lochs-type theorems and approximation properties

In this paper, we study two problems concerning the relationship between regular continued fractions (RCFs) and backward continued fractions (BCFs). The first problem addresses Lochs-type theorems for RCFs and BCFs, where we compare the number of partial quotients in one expansion as a function of the number of partial quotients in the other expansion. The second problem investigates the approximation properties of RCFs and BCFs, with particular attention to the set of irrational numbers that are infinitely often better approximated by BCFs than by RCFs. We show that this set has Lebesgue measure zero and further analyze it from the perspectives of Baire category and fractal dimension.

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.