The relative growth rate of the largest partial quotient to the sum of partial quotients in continued fraction expansions

JOURNAL OF NUMBER THEORY

卷:163

Article

Zhang, Zhenliang¹  Lu, Meiying² 

[1] Henan Inst Sci & Technol, Sch Math Sci, Xinxiang 453003, Peoples R China

[2] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China

关键词: Continued fraction expansion;    The largest partial quotient;    Hausdorff dimension;   

DOI  :  10.1016/j.jnt.2015.11.027

来源: Elsevier

【 摘 要 】

In this paper, we mainly study the growth rate of the largest partial quotient relative to the growth rate of the sum of partial quotients for the continued fraction expansion of an irrational number. We establish that the Hausdorff dimension of the set of points with a given relative growth rate is full. (c) 2016 Elsevier Inc. All rights reserved.

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