GOOD PERMUTATIONS FOR EXTREME DISCREPANCY

被引：73

作者：

FAURE, H ^{[1
]}

机构：

[1] UNIV AIX MARSEILLE 1,F-13331 MARSEILLE 3,FRANCE

来源：

JOURNAL OF NUMBER THEORY | 1992年 / 42卷 / 01期

关键词：

D O I：

10.1016/0022-314X(92)90107-Z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The asymptotic behaviour of the discrepancy of the usual van der Corput sequences in arbitrary base b is known; and the implied constants tend to infinity with the base b. The aim of this paper is, first, to prove that for every base b there exist permutations of the digits such that the constants are less than 1 Log 2 = 1.442... and, second, to produce a permutation, in base b = 36, giving the smallest discrepancy presently known: lim sup( D(N) Log N) = 23 (35 Log 6) = 0.366.... © 1992.

引用

页码：47 / 56

页数：10

共 8 条

[1] DECREASE OF THE DISCREPANCY OF ANY SERIES ON T [J].