二次无理数的Khintchine常数(英文)  

ON THE KHINTCHINE CONSTANTS FOR QUADRATIC IRRATIONALS

作　　者：李兵[1] 

机构地区：[1]华中科技大学数学与统计学院,湖北武汉430074

出　　处：《数学杂志》2010年第2期217-220,共4页Journal of Mathematics

摘　　要：本文研究了二次无理数的Khintchine常数.利用二次无理数的连分数展式,证明了每个二次无理数的p均值Khintchine常数都存在,而且所有二次无理数的p均值Khintchine常数在[1,+∞)上稠密,Khintchine常数也有同样的结果.这样的结果与Lévy常数类似.In this article, we study the Khintchine constants for quadratic irrationals. By the continued fraction expansion of quadratic irrationals, we show that every quadratic irrational has a p-mean Khintchine constant and the set of p-mean Khintchine constants for quadratic irrationals is dense in [1, ＋∞）. Moreover, we have the same results for Khintchine constant. This result is similar to the Levy constant.

关 键 词：连分数 p均值Khintchine常数 Khintchine常数 

分 类 号：O173.2[理学—数学]