Approximating numbers with missing digits by algebraic numbers

被引：5
|
作者：
Kristensen, Simon [1 ]
机构：
[1] Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland
来源：
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2006年 / 49卷
关键词：
diophantine approximation; transcendental numbers; Koksma's classification; Cantor sets; Hausdorff dimension;
D O I：
10.1017/S001309150500057X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that for a given base b and a proper subset E subset of {0,...,b - 1}, #E < b - 1, the set of numbers x E [0, 1] that have no digits from E in their expansion to base b consists almost exclusively of S*-numbers of type at most min{2, log b/log(b - #E)}. We also give upper bounds on the Hausdorff dimension of some exceptional sets.
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页码：657 / 666
页数：10
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