The Hurwitz continued fraction expansion as applied to real numbers

David Simmons

The Hurwitz continued fraction expansion as applied to real numbers

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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).

Original language	English
Number of pages	7
Journal	L’Enseignement Mathématique
Publication status	Accepted/In press - 24 Jun 2016

Keywords

math.NT

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https://arxiv.org/abs/1601.07838

Programme Grant-New Frameworks in metric Number Theory
Velani, S. & Beresnevich, V.
EPSRC
1/06/12 → 30/11/18
Project: Research project (funded) › Research

Cite this

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AB - 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).

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The Hurwitz continued fraction expansion as applied to real numbers

Abstract

Keywords

Access to Document

Projects

Programme Grant-New Frameworks in metric Number Theory

Cite this