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Integer continued fractions for complex numbers

Published 20 Aug 2025 in math.NT | (2508.15078v1)

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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Authors (1)

  1. Cormac O'Sullivan 

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