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arXiv · 1908.00121

Continued fractions over non-Euclidean imaginary quadratic rings

Daniel E. Martin
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Abstract

We propose and study a generalized continued fraction algorithm that can be executed in an arbitrary imaginary quadratic field, the novelty being a non-restriction to the five Euclidean cases. Many hallmark properties of classical continued fractions are shown to be retained, including exponential convergence, best-of-the-second-kind approximation quality (up to a constant), periodicity of quadratic irrational expansions, and polynomial time complexity.

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Daniel E. Martin. 2019-07-31. Continued fractions over non-Euclidean imaginary quadratic rings. https://arxiv.org/abs/1908.00121

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