Best simultaneous diophantine approximations and Levy's theorem

被引：2

作者：

Chevallier, N ^{[1
]}

机构：

[1] Univ Haute Alsace, F-68093 Mulhouse, France

来源：

ANNALES DE L INSTITUT FOURIER | 2005年 / 55卷 / 05期

关键词：

D O I：

10.5802/aif.2134

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

According to Levy's theorem, the denominators of the continued fraction expansion of a real number almost surely grow at most at the rate of a geometric series. We extend this estimate to best simultaneous Diophantine approximations to a set of linear forms.

引用

页码：1635 / +

页数：24

共 50 条

[1] LEVY-KHINTCHIN THEOREM FOR BEST SIMULTANEOUS DIOPHANTINE APPROXIMATIONS
Cheung, Yitwah
Chevallier, Nicolas
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2024, 57 (01): : 185 - 240
[2] Successive minima and best simultaneous diophantine approximations
Aliev, I
Henk, M
MONATSHEFTE FUR MATHEMATIK, 2006, 147 (02): : 95 - 101
[3] Successive Minima and Best Simultaneous Diophantine Approximations
Iskander Aliev
Martin Henk
Monatshefte für Mathematik, 2006, 147 : 95 - 101
[4] BEST SIMULTANEOUS DIOPHANTINE APPROXIMATIONS .2. BEHAVIOR OF CONSECUTIVE BEST APPROXIMATIONS
LAGARIAS, JC
PACIFIC JOURNAL OF MATHEMATICS, 1982, 102 (01) : 61 - 88
[5] On Worley's theorem in Diophantine approximations
Dujella, Andrej
Ibrahimpasic, Bernadin
ANNALES MATHEMATICAE ET INFORMATICAE, 2008, 35 : 61 - 73
[6] Best simultaneous diophantine approximations of Pisot numbers and Rauzy fractals
Hubert, P.
Messaoudi, A.
ACTA ARITHMETICA, 2006, 124 (01) : 1 - 15
[7] Simultaneous diophantine approximations
de Mathan, B
Teulié, O
MONATSHEFTE FUR MATHEMATIK, 2004, 143 (03): : 229 - 245
[8] ON SIMULTANEOUS DIOPHANTINE APPROXIMATIONS
Dyson, F. J.
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1947, 49 : 409 - 420
[9] THE SUBSPACE THEOREM IN DIOPHANTINE APPROXIMATIONS
SCHMIDT, WM
COMPOSITIO MATHEMATICA, 1989, 69 (02) : 121 - 173
[10] On optimal constants for best two-dimensional simultaneous diophantine approximations
Kratz, W
MONATSHEFTE FUR MATHEMATIK, 1999, 128 (02): : 99 - 110

← 1 2 3 4 5 →