DIOPHANTINE APPROXIMATION BY CONTINUED FRACTIONS

被引：3
|
作者：
TONG, JC
机构：
[1] Department of Mathematics and Statistics, University of North Florida, Jacksonville
来源：
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS | 1991年 / 51卷
关键词：
D O I：
10.1017/S1446788700034273
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let zeta be an irrational number with simple continued fraction expansion zeta = [a0; a1,..., a(i),...], p(i)/q(i) be its ith convergent. Let M(i) = [a(i+1); a(i),..., a1] + [0; a(i+2), a(i+3), ...]. In this paper we prove that M(n-1) < r and M(n) < R imply M(n+1) > 1 /(r-1 + a(n+1) square-root 1 - 4/(rR)-a(n+1)2R-1), which generalizes a previous result of the author.
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页码：324 / 330
页数：7
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