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arXiv · 2610.30621

Norm-Euclideanity in cyclic fields

Gustav Kjærbye Bagger
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Abstract

Consider a cyclic number field of prime degree $p$. For a fixed degree, there are only finitely many such fields which are norm-Euclidean. When $p=2$ or $3$, these have been completely determined. If instead $p>3$, one can bound the discriminant of such fields from above. We substantially sharpen these upper bounds via an explicit Burgess-type criterion and describe a method for completely resolving other small prime cases.

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Gustav Kjærbye Bagger. 2026-10-22. Norm-Euclideanity in cyclic fields. https://arxiv.org/abs/2610.30621

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