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

页码：547 / 565

页数：19

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