Integer continued fractions for complex numbers
Number Theory
2025-08-22 v1
Abstract
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.
Cite
@article{arxiv.2508.15078,
title = {Integer continued fractions for complex numbers},
author = {Cormac O'Sullivan},
journal= {arXiv preprint arXiv:2508.15078},
year = {2025}
}
Comments
21 pages and 10 figures