The Hurwitz continued fraction expansion as applied to real numbers

被引：2
|
作者：
Simmons, David [1 ]
机构：
[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England
来源：
ENSEIGNEMENT MATHEMATIQUE | 2016年 / 62卷 / 3-4期
基金：
英国工程与自然科学研究理事会;
关键词：
Continued fraction expansion; Diophantine approximation;
D O I：
10.4171/LEM/62-3/4-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Hurwitz (1887) defined a continued fraction algorithm for complex numbers which is better behaved in many respects than a more "natural" extension of the classical continued fraction algorithm to the complex plane would be. Although the Hurwitz complex continued fraction algorithm is not "reducible" to another complex continued fraction algorithm, over the reals the story is different. In this note we make clear the relation between the restriction of Hurwitz's algorithm to the real numbers and the classical continued fraction algorithm. As an application we reprove the main result of Choudhuri and Dani (2015).
引用
收藏
页码：475 / 485
页数：11
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