ON THE LARGEST PARTIAL QUOTIENTS IN CONTINUED FRACTION EXPANSIONS-Reference-Cited by-同舟云学术

ON THE LARGEST PARTIAL QUOTIENTS IN CONTINUED FRACTION EXPANSIONS

Published:2021-04-23 Issue:04 Volume:29 Page:2150099
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

FANG LULU¹²,LIU JIAN³

Affiliation:

1. School of Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

2. School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China

3. College of Information Engineering, Nanjing University of Finances and Economics, Nanjing 210023, P. R. China

Abstract

Let [Formula: see text] be the continued fraction expansion of an irrational [Formula: see text]. For any [Formula: see text], write [Formula: see text]. This paper is concerned with the Hausdorff dimension of the set [Formula: see text] where [Formula: see text] is a function such that [Formula: see text] as [Formula: see text]. We calculate the Hausdorff dimension of [Formula: see text] for a very large class of functions with certain growth rates, which improves the existing results of Wu and Xu (2009), Liao and Rams (2016) and Chang and Chen (2018).

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X21500997

Reference18 articles.

1. Metrical Theory of Continued Fractions

2. THE DISTRIBUTION OF THE LARGEST COEFFICIENT IN CONTINUED FRACTION EXPANSIONS

3. A conjecture of Erdös on continued fractions

4. Sur l'ordre de grandeur des quotients partiels du développement en fractions continues régulières

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