Norm-Euclidean cyclic fields of prime degree

Citeable URL: https://ir.library.oregonstate.edu/concern/articles/vh53ww37b

Descriptions

Attribute Name	Values
Creator	McGown, Kevin J.
Abstract	Let K be a cyclic number field of prime degree ℓ. Heilbronn showed that for a given ℓ there are only finitely many such fields that are norm-Euclidean. In the case of ℓ = 2 all such norm-Euclidean fields have been identified, but for ℓ ≠ 2, little else is known. We give the first upper bounds on the discriminants of such fields when ℓ > 2. Our methods lead to a simple algorithm which allows one to generate a list of candidate norm-Euclidean fields up to a given discriminant, and we provide some computational results. This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by World Scientific Publishing Co. and can be found at: http://www.worldscientific.com/worldscinet/ijnt. Keywords: cubic fields, cyclic fields, Norm-Euclidean, character sums
Resource Type	Article
DOI	https://doi.org/10.1142/S1793042112500133
Date Available	2012-12-21T23:29:02+00:00
Date Issued	2012-02
Citation	McGown, K. (2012). NORM-EUCLIDEAN CYCLIC FIELDS OF PRIME DEGREE. INTERNATIONAL JOURNAL OF NUMBER THEORY, 8(1), 227-254. doi: 10.1142/S1793042112500133
Journal Title	International Journal of Number Theory
Journal Volume	8
Journal Issue/Number	1
Academic Affiliation	Mathematics
Rights Statement	Copyright Not Evaluated
Publisher	World Scientific Publishing Co.
Peer Reviewed	Yes
Language	English [eng]
Replaces	http://hdl.handle.net/1957/35848