GOOD APPROXIMATIONS AND CONTINUED FRACTIONS

被引：31

作者：

KRAAIKAMP, C ^{[1
]}

LIARDET, P ^{[1
]}

机构：

[1] UNIV AIX MARSEILLE 1,CNRS,URA 225,F-13331 MARSEILLE 3,FRANCE

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1991年 / 112卷 / 02期

关键词：

CONTINUED FRACTIONS; DIOPHANTINE APPROXIMATIONS;

D O I：

10.2307/2048720

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (q(n))n be the sequence of best approximation denominators of an irrational number alpha. The set of real numbers x for which q(n)x --> 0 (mod 1) is studied. It is shown that a number x belongs to alpha-Z (mod 1) if and only if a simple condition on the speed of the convergence related to an arithmetic property of alpha-is satisfied. This set is uncountable whenever alpha-has unbounded partial quotients.

引用

页码：303 / 309

页数：7