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arXiv · 2508.15078

Integer continued fractions for complex numbers

Cormac O'Sullivan
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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.

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Cormac O'Sullivan. 2025-08-20. Integer continued fractions for complex numbers. https://arxiv.org/abs/2508.15078

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