Integer continued fractions for complex numbers

Fuente: arXiv
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Auteur principal: O'Sullivan, Cormac
Format: Preprint
Publié: 2025
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author O'Sullivan, Cormac
author_facet O'Sullivan, Cormac
contents We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new representations are shown to be unique, and to have useful properties. They also admit a geometric cutting sequence interpretation.
format Preprint
id arxiv_https___arxiv_org_abs_2508_15078
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Integer continued fractions for complex numbers
O'Sullivan, Cormac
Number Theory
11Y65, 11F06, 11H55
We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new representations are shown to be unique, and to have useful properties. They also admit a geometric cutting sequence interpretation.
title Integer continued fractions for complex numbers
topic Number Theory
11Y65, 11F06, 11H55
url https://arxiv.org/abs/2508.15078