farey -子图与连分数

IF 0.4 4区数学 Q4 MATHEMATICS

Studia Scientiarum Mathematicarum Hungarica Pub Date : 2021-06-28 DOI:10.1556/012.2022.01525

S. Kushwaha, R. Sarma

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引用次数: 3

摘要

在这篇文章中，我们研究了Farey图的一组子图，对于每一个N∈N，我们将其记为_ (N)。我们证明了当且仅当N等于1或一个素数幂时，N是连通的。我们引入一类连分数，称为_ (N) -对于每个N > 1的连分数。建立了图_ _ N中_ _ N连分式与无穷远处若干路径之间的关系。利用这种对应关系，讨论了实数的连分数展开式的存在唯一性。

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Farey-Subgraphs and Continued Fractions

In this article, we study a family of subgraphs of the Farey graph, denoted as ℱN for every N ∈ ℕ. We show that ℱN is connected if and only if N is either equal to one or a prime power. We introduce a class of continued fractions referred to as ℱN -continued fractions for each N > 1. We establish a relation between ℱN-continued fractions and certain paths from infinity in the graph ℱN. Using this correspondence, we discuss the existence and uniqueness of ℱN-continued fraction expansions of real numbers.

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来源期刊

Studia Scientiarum Mathematicarum Hungarica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research papers on various fields of mathematics, e.g., algebra, algebraic geometry, analysis, combinatorics, dynamical systems, geometry, mathematical logic, mathematical statistics, number theory, probability theory, set theory, statistical physics and topology.