An L(1/3) algorithm for ideal class group and regulator computation in certain number fields
| hal.structure.identifier | Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX] | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| dc.contributor.author | BIASSE, Jean-François | |
| dc.date.accessioned | 2024-04-04T02:31:12Z | |
| dc.date.available | 2024-04-04T02:31:12Z | |
| dc.date.issued | 2014 | |
| dc.identifier.issn | 0025-5718 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190288 | |
| dc.description.abstractEn | We analyse the complexity of the computation of the class group structure, regulator, and a system of fundamental units of a certain class of number fields. Our approach differs from Buchmann's, who proved a complexity bound of L(1/2,O(1)) when the discriminant tends to infinity with fixed degree. We achieve a subexponential complexity in O(L(1/3,O(1))) when both the discriminant and the degree of the extension tend to infinity by using techniques due to Enge and Gaudry in the context of algebraic curves over finite fields. | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.title.en | An L(1/3) algorithm for ideal class group and regulator computation in certain number fields | |
| dc.type | Article de revue | |
| dc.subject.hal | Informatique [cs]/Cryptographie et sécurité [cs.CR] | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 0912.1927 | |
| bordeaux.journal | Mathematics of Computation | |
| bordeaux.page | 2005-2031 | |
| bordeaux.volume | 83 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 288 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | inria-00440223 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00440223v1 | |
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