Continued fractions with low complexity: transcendence measures and quadratic approximation

被引：12
作者：
Bugeaud, Yann [1 ]
机构：
[1] Univ Strasbourg, F-67084 Strasbourg, France
来源：
COMPOSITIO MATHEMATICA | 2012年 / 148卷 / 03期
关键词：
continued fraction; transcendence; Schmidt's subspace theorem; DIOPHANTINE APPROXIMATION; ALGEBRAIC-NUMBERS; REAL NUMBERS; MAHLERS CLASSIFICATION; IRRATIONALITY MEASURES; SYMBOLIC DYNAMICS; KOKSMAS; WORDS;
D O I：
10.1112/S0010437X11007524
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We establish measures of non-quadraticity and transcendence measures for real numbers whose sequence of partial quotients has sublinear block complexity. The main new ingredient is an improvement of Liouville's inequality giving a lower bound for the distance between two distinct quadratic real numbers. Furthermore, we discuss the gap between Mahler's exponent w(2) and Koksma's exponent w(2)*
引用
收藏
页码：718 / 750
页数：33
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