On corner avoidance of β-adic Halton sequences

被引：0

作者：

Hofer, Markus ^{[1
]}

Ziegler, Volker ^{[2
]}

机构：

[1] Graz Univ Technol, Inst Math A, Steyrergasse 30, A-8010 Graz, Austria

[2] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math RICAM, Altenbergerstr 69, A-4040 Linz, Austria

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2016年 / 195卷 / 03期

基金：

奥地利科学基金会;

关键词：

Corner avoidance; Uniform distribution; Beta-expansion; Numerical integration; Subspace theorem; SUBSPACE THEOREM; NUMERATION; SYSTEMS;

D O I：

10.1007/s10231-015-0499-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the corner avoiding property of s-dimensional beta-adic Halton sequences. After extending this class of point sequences in an intuitive way, we show that the hyperbolic distance between each element of the sequence and the closest corner of [0,1)(s) is O (1/Ns/2+epsilon), where N denotes the index of the element. In our proof, we use tools from Diophantine analysis; more precisely, we apply Schmidt's subspace theorem.

引用

页码：957 / 975

页数：19

共 20 条

[1] [Anonymous], 1997, LECT NOTES MATH
[2] A further improvement of the Quantitative Subspace Theorem
Evertse, J-H.
Ferretti, R. G.
[J]. ANNALS OF MATHEMATICS, 2013, 177 (02) : 513 - 590
[3] Evertse JH, 2002, J REINE ANGEW MATH, V548, P21
[4] SYSTEMS OF NUMERATION
FRAENKEL, AS
[J]. AMERICAN MATHEMATICAL MONTHLY, 1985, 92 (02) : 105 - 114
[5] FINITE BETA-EXPANSIONS
FROUGNY, C
SOLOMYAK, B
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1992, 12 : 713 - 723
[6] Grabner P., 2012, UNIF DISTRIB THEORY, V7, P11
[7] GRABNER PJ, 1995, ACTA ARITH, V70, P103
[8] HARDER G, 1999, FUNDAMENTAL PRINCIPL, V322
[9] Hartinger J., 2005, INTEGERS, V5, P16
[10] On corner avoidance properties of random-start Halton sequences
Hartinger, Jurgen
Ziegler, Volker
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (03) : 1109 - 1121

← 1 2 →