MULTIFRACTAL ANALYSIS OF CONVERGENCE EXPONENTS FOR PRODUCTS OF CONSECUTIVE PARTIAL QUOTIENTS IN CONTINUED FRACTIONS

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外文摘要：For each real number x ∈(0,1),let[a1(x),a2(x),…,an(x),…]denote its con-tinued fraction expansion.We study the convergence exponent defined byτ(x):=inf{s≥ 0:∞Σn=1(an(x)an+1(x))-s＜∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets of r(x)are determined.

外文关键词：

continued fractionsproduct of partial quotientsHausdorff dimension

作者：

房路路、马际华、宋昆昆、杨欣

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作者单位：

School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210094,China

School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China

Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education),School of Mathematics and Statistics,Hunan Normal University,Changsha 410081,China

基金：

Scientific Research Fund of Hunan Provincial Education DepartmentNatural Science Foundation of Jiangsu ProvinceFundamental Research Funds for the Centra UniversitiesNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of China

项目编号：

21B0070BK2023145230922010809118015911197119512071171121711071220120712371072

出版年：

2024

DOI：

10.1007/s10473-024-0422-6

数学物理学报(英文版)

中科院武汉物理与数学研究所

数学物理学报(英文版)

CSTPCD

影响因子：0.256

ISSN：0252-9602

年,卷(期)：2024.44(4)