Diophantine approximation of Mahler numbers

被引：8

作者：

Bell, Jason P. ^{[1
]}

Bugeaud, Yann ^{[2
]}

Coons, Michael ^{[3
]}

机构：

[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada

[2] Univ Strasbourg, Dept Math, F-67084 Strasbourg, France

[3] Univ Newcastle, Sch Math & Phys Sci, Callaghan, NSW 2308, Australia

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2015年 / 110卷

基金：

加拿大自然科学与工程研究理事会; 澳大利亚研究理事会; 奥地利科学基金会;

关键词：

QUILLEN-SUSLIN THEOREM; ALGEBRAIC-NUMBERS; REAL NUMBERS; ARITHMETIC CHARACTERISTICS; IRRATIONALITY MEASURES; FUNCTIONAL-EQUATIONS; REGULAR SEQUENCES; COMPLEXITY; AUTOMATA; SERIES;

D O I：

10.1112/plms/pdv016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose that F(x) is an element of Z[[x]] is a Mahler function and that 1/b is in the radius of convergence of F(x) for an integer b >= 2. In this paper, we consider the approximation of F(1/b) by algebraic numbers. In particular, we prove that F(1/b) cannot be a Liouville number. If, in addition, F(x) is regular, we show that F(1/b) is either rational or transcendental, and in the latter case that F(1/b) is an S-number or a T-number in Mahler's classification of real numbers.

引用

页码：1157 / 1206

页数：50

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