Continued fractions with partial quotients bounded in average

被引：0
作者：
Cooper, Joshua N. [1 ]
机构：
[1] Univ S Carolina, Dept Math, LeConte Coll, Columbia, SC 29208 USA
来源：
FIBONACCI QUARTERLY | 2006年 / 44卷 / 04期
关键词：
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We ask, for which n does there exists a k, 1 <= k <= n and (k, n) = 1, so that k/n has a continued fraction whose partial quotients are bounded in average by a constant B? This question is intimately connected with several other well-known problems, and we provide a lower bound in the case of B = 2. The proof, which is completely elementary, involves a simple "shifting" argument, the Catalan numbers, and the solution to a linear recurrence.
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页码：297 / 301
页数：5
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