The Euclidean algorithm in quintic and septic cyclic fields
| hal.structure.identifier | Laboratoire de Mathématiques Blaise Pascal [LMBP] | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| dc.contributor.author | LEZOWSKI, Pierre | |
| hal.structure.identifier | Department of Mathematics and Statistics [Chico] | |
| dc.contributor.author | MCGOWN, Kevin | |
| dc.date.accessioned | 2024-04-04T03:14:52Z | |
| dc.date.available | 2024-04-04T03:14:52Z | |
| dc.date.created | 2016-03-19 | |
| dc.date.issued | 2017-09-01 | |
| dc.identifier.issn | 0025-5718 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194103 | |
| dc.description.abstractEn | Conditionally on the Generalized Riemann Hypothesis (GRH), we prove the following results: (1) a cyclic number field of degree $5$ is norm-Euclidean if and only if $\Delta=11^4,31^4,41^4$; (2) a cyclic number field of degree $7$ is norm-Euclidean if and only if $\Delta=29^6,43^6$; (3) there are no norm-Euclidean cyclic number fields of degrees $19$, $31$, $37$, $43$, $47$, $59$, $67$, $71$, $73$, $79$, $97$. Our proofs contain a large computational component, including the calculation of the Euclidean minimum in some cases; the correctness of these calculations does not depend upon the GRH. Finally, we improve on what is known unconditionally in the cubic case by showing that any norm-Euclidean cyclic cubic field must have conductor $f\leq 157$ except possibly when $f\in(2\cdot 10^{14}, 10^{50})$. | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.title.en | The Euclidean algorithm in quintic and septic cyclic fields | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1090/mcom/3169 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1601.03433 | |
| bordeaux.journal | Mathematics of Computation | |
| bordeaux.page | 2535--2549 | |
| bordeaux.volume | 86 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 307 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01258906 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01258906v1 | |
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