Norm relations and computational problems in number fields
| hal.structure.identifier | University of South Florida [Tampa] [USF] | |
| dc.contributor.author | BIASSE, Jean‐françois | |
| hal.structure.identifier | Technische Universität Kaiserslautern [TU Kaiserslautern] | |
| dc.contributor.author | FIEKER, Claus | |
| hal.structure.identifier | Technical University of Kaiserslautern [TU Kaiserslautern] | |
| dc.contributor.author | HOFMANN, Tommy | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut National de Recherche en Informatique et en Automatique [Inria] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | PAGE, Aurel | |
| dc.date.accessioned | 2024-04-04T02:55:48Z | |
| dc.date.available | 2024-04-04T02:55:48Z | |
| dc.date.created | 2021-07-14 | |
| dc.date.issued | 2022-06 | |
| dc.identifier.issn | 0024-6107 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192399 | |
| dc.description.abstractEn | For a finite group $G$, we introduce a generalization of norm relations in the group algebra $\mathbb{Q}[G]$. We give necessary and sufficient criteria for the existence of such relations and apply them to obtain relations between the arithmetic invariants of the subfields of an algebraic number field with Galois group $G$. On the algorithm side this leads to subfield based algorithms for computing rings of integers, $S$-unit groups and class groups. For the $S$-unit group computation this yields a polynomial-time reduction to the corresponding problem in subfields. We compute class groups of large number fields under GRH, and new unconditional values of class numbers of cyclotomic fields. | |
| dc.description.sponsorship | Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008 | |
| dc.language.iso | en | |
| dc.publisher | London Mathematical Society ; Wiley | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.title.en | Norm relations and computational problems in number fields | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1112/jlms.12563 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Informatique [cs]/Calcul formel [cs.SC] | |
| dc.subject.hal | Mathématiques [math]/Théorie des groupes [math.GR] | |
| dc.subject.hal | Mathématiques [math]/Théorie des représentations [math.RT] | |
| dc.identifier.arxiv | 2002.12332 | |
| bordeaux.journal | Journal of the London Mathematical Society | |
| bordeaux.page | 2373-2414 | |
| bordeaux.volume | 105 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02497890 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02497890v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20the%20London%20Mathematical%20Society&rft.date=2022-06&rft.volume=105&rft.issue=4&rft.spage=2373-2414&rft.epage=2373-2414&rft.eissn=0024-6107&rft.issn=0024-6107&rft.au=BIASSE,%20Jean%E2%80%90fran%C3%A7ois&FIEKER,%20Claus&HOFMANN,%20Tommy&PAGE,%20Aurel&rft.genre=article |
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