Lüroth展式相邻字符乘积的部分和的相关例外集的分形维数  

Hausdorff Dimension of Related Exceptional Sets of Sums of Products of Consecutive Digits of Lüroth Expansions

作　　者：张一鸣 ZHANG Yi-ming(College of Mathematical Science,Chongqing Normal University,Shapingba401331,Chongqing)

机构地区：[1]重庆师范大学数学科学学院,重庆沙坪坝401331

出　　处：《商洛学院学报》2023年第6期37-42,共6页Journal of Shangluo University

摘　　要：为了研究Lüroth展式相邻字符乘积的部分和的增长速度问题,在给定增长速度的情况下,利用Cantor子集和覆盖的维数结果,给出了相关例外集的Hausdorff维数结果,主要包括Lüroth展式相邻字符乘积的部分和的双指数增长的情况下的维数结果,该结果扩展了数的表示理论与分形维数的交叉研究。To study the growth rate of sums of products of consecutive partial quotients of Lüroth expansions,given the growth rate,the Hausdorff dimension results of the related exceptional set are given by using the dimensions of the Cantor subset and the cover sets,mainly including the case of double exponential growth of sums of products of consecutive digits in the Lüroth expansions.These results expands the crossover study of the representation theory of numbers and the fractal dimension.

关 键 词：Lüroth展式 例外集 HAUSDORFF维数 

分 类 号：O156[理学—数学]