On the transcendence of real numbers with a regular expansion

被引：9

作者：

Adamczewski, B ^{[1
]}

Cassaigne, J ^{[1
]}

机构：

[1] CNRS, UPR 9016, Math Inst, F-13288 Marseille 09, France

来源：

JOURNAL OF NUMBER THEORY | 2003年 / 103卷 / 01期

关键词：

transcendence; coding of rotation; three-interval exchange;

D O I：

10.1016/S0022-314X(03)00054-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply the Ferenczi-Mauduit combinatorial condition obtained via a reformulation of Ridout's theorem to prove that a real number whose b-ary expansion is the coding of an irrational rotation on the circle with respect to a partition in two intervals is transcendental. We also prove the transcendence of real numbers whose b-ary expansion arises from a non-periodic three-interval exchange transformation. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：27 / 37

页数：11

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