Integer continued fractions for complex numbers

2025/08/20 by Cormac O'Sullivan, O'Sullivan, Cormac · 2 voices
#math.NT

paper · pdf · doi:10.48550/arxiv.2508.15078

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.

Discussions

• Integer continued fractions for complex numbers [hn, 53 points, 2 comments]
• Integer continued fractions for complex numbers https://arxiv.org/abs/2508.15078 [bsky, 0 points, 0 comments]

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