On the complexity of algebraic numbers.

被引：52
作者：
Adamczewski, B
Bugeaud, Y
Luca, F
机构：
[1] Univ Paris 11, UMR 8623, Rech Informat Lab, F-91405 Orsay, France
[2] Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58180, Michoacan, Mexico
[3] Univ Strasbourg 1, UFR Math, F-67084 Strasbourg, France
来源：
COMPTES RENDUS MATHEMATIQUE | 2004年 / 339卷 / 01期
关键词：
D O I：
10.1016/j.crma.2004.04.012
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
On the complexity of algebraic numbers. Let b greater than or equal to 2 be an integer. We prove that real numbers whose b-ary expansion satisfies some given, simple, combinatorial condition are transcendental. This implies that the b-ary expansion of any algebraic irrational number cannot be generated by a finite automaton.
引用
收藏
页码：11 / 14
页数：4
相关论文
共 19 条
[1]   A Liouville-like approach for the transcendence of some real numbers [J].
Adamczewski, B .
COMPTES RENDUS MATHEMATIQUE, 2004, 338 (07) :511-514
[2]   On the transcendence of real numbers with a regular expansion [J].
Adamczewski, B ;
Cassaigne, J .
JOURNAL OF NUMBER THEORY, 2003, 103 (01) :27-37
[3]  
ADAMCZEWSKI B, 2004, ON COMPLEXITY ALGEBR
[4]   Algebraic irrational binary numbers cannot be fixed points of non-trivial constant length or primitive morphisms [J].
Allouche, JP ;
Zamboni, LQ .
JOURNAL OF NUMBER THEORY, 1998, 69 (01) :119-124
[5]  
BOREL E, 1950, CR HEBD ACAD SCI, V230, P591
[6]  
Cobham A., 1972, MATH SYST THEORY, V6, P164, DOI 10.1007/BF01706087
[7]   Transcendence of numbers with a low complexity expansion [J].
Ferenczi, S ;
Mauduit, C .
JOURNAL OF NUMBER THEORY, 1997, 67 (02) :146-161
[8]   ON COMPUTATIONAL COMPLEXITY OF ALGORITHMS [J].
HARTMANIS, J ;
STEARNS, RE .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 117 (05) :285-+
[9]  
LOXTON JH, 1988, J REINE ANGEW MATH, V392, P57
[10]   Arithmetic characteristics of category of functional equation solution [J].
Mahler, K .
MATHEMATISCHE ANNALEN, 1929, 101 :342-366
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