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

[21] THE SIGNATURES OF THE ERRORS OF SIMULTANEOUS DIOPHANTINE APPROXIMATIONS
ROGERS, CA
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1948, 54 (01) : 81 - 81
[22] SPECIALLY STRUCTURED SIMULTANEOUS DIOPHANTINE APPROXIMATIONS
MULLIN, AA
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (06): : A612 - A613
[23] On simultaneous diophantine approximations to ζ(2) and ζ(3)
Dauguet, Simon
Zudilin, Wadim
JOURNAL OF NUMBER THEORY, 2014, 145 : 362 - 387
[24] SIMULTANEOUS DIOPHANTINE APPROXIMATIONS AND CUBIC IRRATIONALS
ADAMS, WW
PACIFIC JOURNAL OF MATHEMATICS, 1969, 30 (01) : 1 - &
[25] On simultaneous Diophantine approximations. Vectors of given Diophantine type
Moshchevitin, NG
MATHEMATICAL NOTES, 1997, 61 (5-6) : 590 - 599
[26] On simultaneous diophantine approximations. Vectors of given diophantine type
N. G. Moshchevitin
Mathematical Notes, 1997, 61 : 590 - 599
[27] On best simultaneous approximations
Moshchevitin, NG
RUSSIAN MATHEMATICAL SURVEYS, 1996, 51 (06) : 1214 - 1215
[28] GENERALIZATIONS OF KY FAN’S THEOREM ON BEST APPROXIMATIONS
T. D. Narang
Analysis in Theory and Applications, 2009, 25 (02) : 109 - 116
[29] Simultaneous diophantine approximations with nonmonotonic error function
Budarina, N. V.
DOKLADY MATHEMATICS, 2011, 83 (02) : 194 - 196
[30] A NOTE ON BEST AND BEST SIMULTANEOUS APPROXIMATIONS
MUTHUKUMAR, S
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1980, 11 (06) : 715 - 719

← 1 2 3 4 5 →