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

作　　者：Lulu FANG Jihua MA Kunkun SONG Xin YANG 房路路;马际华;宋昆昆;杨欣(School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing210094,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)

机构地区：[1]School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing210094,China [2]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China [3]Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education),School of Mathematics and Statistics,Hunan Normal University,Changsha 410081,China

出　　处：《Acta Mathematica Scientia》2024年第4期1594-1608,共15页数学物理学报（B辑英文版）

基　　金：supported by the Scientific Research Fund of Hunan Provincial Education Department(21B0070);the Natural Science Foundation of Jiangsu Province(BK20231452);the Fundamental Research Funds for the Central Universities(30922010809);the National Natural Science Foundation of China(11801591,11971195,12071171,12171107,12201207,12371072)。

摘　　要：For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+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 ofτ(x)are determined.

关 键 词：continued fractions product of partial quotients Hausdorff dimension 

分 类 号：O156[理学—数学]