Shrinking the period lengths of continued fractions while still capturing convergents

被引：20

作者：

Burger, Edward B. ^{[1
]}

Gell-Redirian, Jesse ^{[1
]}

Kravitz, Ross ^{[1
]}

Walton, Daniel ^{[1
]}

Yates, Nicholas ^{[1
]}

机构：

[1] Williams Coll, Dept Math, Williamstown, MA 01267 USA

来源：

JOURNAL OF NUMBER THEORY | 2008年 / 128卷 / 01期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1016/j.jnt.2007.03.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Here we prove that every real quadratic irrational alpha can be expressed as a periodic non-simple continued fraction having period length one. Moreover, we show that the sequence of rational numbers generated by successive truncations of this expansion is a sequence of convergents of alpha. We close with an application relating the structure of a quadratic alpha to its conjugate. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：144 / 153

页数：10

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