On the Littlewood conjecture in simultaneous diophantine approximation

被引：18
作者：
Adamczewski, Boris
Bugeaud, Yann
机构：
[1] Univ Lyon 1, CNRS, Inst Camille Jordan, F-69622 Villeurbanne, France
[2] Univ Strasbourg 1, UFR Math, F-67084 Strasbourg, France
来源：
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2006年 / 73卷
关键词：
D O I：
10.1112/S0024610706022617
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For any given real number alpha with bounded partial quotients, we construct explicitly continuum many real numbers beta with bounded partial quotients for which the pair (alpha,beta) satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.
引用
收藏
页码：355 / 366
页数：12
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