A note on approximation efficiency and partial quotients of Engel continued fractions

被引：4

作者：

Hu, Hui ^{[1
]}

Yu, Yueli ^{[2
]}

Zhao, Yanfen ^{[2
]}

机构：

[1] Nanchang Hongkong Univ, Sch Math & Informat Sci, Nanchang 330063, Jiangxi, Peoples R China

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2017年 / 13卷 / 09期

关键词：

Engel continued fraction; best approximation; partial quotient; Hausdorff dimension; DIMENSION; EXPANSION; NUMBERS; SETS;

D O I：

10.1142/S1793042117501329

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

consider the efficiency of approximating real numbers by their convergents of Engel continued fractions (ECF). Specifically, we estimate the Hausdorff dimension of the set of points whose ECF-convergents are the best approximations infinitely often. We also obtain the Hausdorff dimensions of the Jarnik-like set and the related sets defined by some growth rates of partial quotients in ECF expansions.

引用

页码：2433 / 2443

页数：11

共 14 条

[1]

Besicovitch A.S., 1934, J London Math Soc, V9, P126, DOI DOI 10.1112/JLMS/S1-9.2.126

[2] Sets of exact approximation order by rational numbers [J].