形式级数域上Sylvester级数展式中例外集的维数  

The Dimensions of Exceptional Sets in Sylvester Series Expansions of Formal Laurent Series

作　　者：傅毅 FU Yi(College of Mathematical Science,Chongqing Normal University,Shapingba 401331,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》2025年第2期30-33,38,共5页Journal of Shangluo University

基　　金：重庆市自然科学基金面上项目(CSTB2022NSCQ-MSX0445)。

摘　　要：为了研究形式级数域上Sylvester级数展式部分商的次数和的增长速度问题,利用Moran集的维数结果及集合的自然覆盖计算其盒维数,给出了相关例外集的维数结果,主要包括一般函数增长速度的例外集的Hausdorff维数。进一步作为应用,同时给出了以多项式和指数速度增长时,相关例外集的Hausdorff维数结果,扩展了形式级数域上Sylvester级数展式的维数研究。In order to study the growth rate of the order of Sylvester series expansion characters over formal power series fields,the dimension results of Moran sets and calculate their box dimension were utilized through natural coverings.Relevant dimension results for exceptional sets,mainly including the Hausdorff dimension of exceptional sets for general function growth rates were provided.Furthermore,as an application,the Hausdorff dimension results of related exceptional sets were presented when growth occurs at polynomial and exponential rates,thereby extending the dimensional study of Sylvester series expansions over formal power series fields.

关 键 词：形式级数域 Sylvester级数展式 例外集 HAUSDORFF维数 

分 类 号：O156.7[理学—数学]