The determination of norm-Euclidean cyclic cubic fields
Number Theory
2025-07-09 v1
Abstract
It is known on the Generalised Riemann Hypothesis that there are precisely cyclic cubic fields that are norm-Euclidean. Unconditionally, there is a gap between analytic estimates which hold for all sufficiently large conductors and computational techniques. In this paper, we establish new results concerning explicit bounds for cubic non-residues and refine previous computational techniques, enabling us to completely characterise all norm-Euclidean cyclic cubic fields.
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Cite
@article{arxiv.2507.05862,
title = {The determination of norm-Euclidean cyclic cubic fields},
author = {Gustav Kjærbye Bagger and Andrew R. Booker and Bryce Kerr and Kevin McGown and Valeriia Starichkova and Tim Trudgian},
journal= {arXiv preprint arXiv:2507.05862},
year = {2025}
}
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24 pages