On the complexity of algebraic numbers I. Expansions in integer bases

被引：97
|
作者：
Adamczewski, Boris [1 ]
Bugeaud, Yann
机构：
[1] Univ Lyon 1, CNRS, F-69622 Villeurbanne, France
[2] Univ Strasbourg, F-67000 Strasbourg, France
来源：
ANNALS OF MATHEMATICS | 2007年 / 165卷 / 02期
关键词：
D O I：
10.4007/annals.2007.165.547
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let b > 2 be an integer. We prove that the b-ary expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendence criterion.
引用
收藏
页码：547 / 565
页数：19
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