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.

引用

页码：297 / 301

页数：5

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