PreprintarXiv licencearXiv
Norm-Euclideanity in cyclic fields
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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BibTeX
@misc{bagger2026normeuclideanity,
title = {{Norm-Euclideanity in cyclic fields}},
author = {Gustav Kjærbye Bagger},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30621},
eprint = {2610.30621},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30621},
}
RIS
TY - UNPB
TI - Norm-Euclideanity in cyclic fields
AU - Gustav Kjærbye Bagger
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30621
UR - https://arxiv.org/abs/2610.30621
AB - 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.
ER -