Norm-Euclidean cyclic fields of prime degree Public Deposited

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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.

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  • 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.
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  • McGown, K. (2012). NORM-EUCLIDEAN CYCLIC FIELDS OF PRIME DEGREE. INTERNATIONAL JOURNAL OF NUMBER THEORY, 8(1), 227-254. doi: 10.1142/S1793042112500133
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  • description.provenance : Approved for entry into archive by Deanne Bruner(deanne.bruner@oregonstate.edu) on 2012-12-21T23:29:02Z (GMT) No. of bitstreams: 1 McGownKevinMathematicsNormEuclideanCyclic.pdf: 259312 bytes, checksum: f288ee3712ef6d64b8fbfc25e4ad8ebd (MD5)
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  • description.provenance : Submitted by Deanne Bruner (deanne.bruner@oregonstate.edu) on 2012-12-20T00:42:17Z No. of bitstreams: 1 McGownKevinMathematicsNormEuclideanCyclic.pdf: 259312 bytes, checksum: f288ee3712ef6d64b8fbfc25e4ad8ebd (MD5)

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