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
收藏
页码：2433 / 2443
页数：11
相关论文
共 50 条
  • [31] Continued fractions with bounded even-order partial quotients
    Hancl, Jaroslav
    Turek, Ondrej
    RAMANUJAN JOURNAL, 2023, 62 (01): : 69 - 110
  • [32] Increasing rate of weighted product of partial quotients in continued fractions
    Bakhtawar, Ayreena
    Feng, Jing
    CHAOS SOLITONS & FRACTALS, 2023, 172
  • [33] METRIC THEORY of PARTIAL QUOTIENTS of N-CONTINUED FRACTIONS
    Wang, Jinfeng
    Zhang, Yuan
    Fractals, 2022, 30 (01):
  • [34] Continued fractions with bounded even-order partial quotients
    Jaroslav Hančl
    Ondřej Turek
    The Ramanujan Journal, 2023, 62 : 69 - 110
  • [35] HEILBRONN,A. THEOREM FOR CONTINUED FRACTIONS WITH ODD PARTIAL QUOTIENTS
    RIEGER, GJ
    MATHEMATISCHE NACHRICHTEN, 1981, 101 : 295 - 307
  • [36] The growth rate of the partial quotients in a class of continued fractions with parameters
    Zhong, Ting
    Tang, Liang
    JOURNAL OF NUMBER THEORY, 2014, 145 : 388 - 401
  • [37] Metric properties of the product of consecutive partial quotients in continued fractions
    Lingling Huang
    Jun Wu
    Jian Xu
    Israel Journal of Mathematics, 2020, 238 : 901 - 943
  • [38] METRIC THEORY OF PARTIAL QUOTIENTS OF N-CONTINUED FRACTIONS
    Wang, Jinfeng
    Zhang, Yuan
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2022, 30 (01)
  • [39] LIMIT-THEOREMS FOR SUMS OF PARTIAL QUOTIENTS OF CONTINUED FRACTIONS
    PHILIPP, W
    MONATSHEFTE FUR MATHEMATIK, 1988, 105 (03): : 195 - 206
  • [40] Metric properties of the product of consecutive partial quotients in continued fractions
    Huang, Lingling
    Wu, Jun
    Xu, Jian
    ISRAEL JOURNAL OF MATHEMATICS, 2020, 238 (02) : 901 - 943
12345