Computing the residue of the Dedekind zeta function
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| dc.contributor.author | BELABAS, Karim | |
| hal.structure.identifier | Universidad de Santiago de Chile [Santiago] [USACH] | |
| dc.contributor.author | FRIEDMAN, Eduardo | |
| dc.date.accessioned | 2024-04-04T02:20:44Z | |
| dc.date.available | 2024-04-04T02:20:44Z | |
| dc.date.created | 2013-04-30 | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0025-5718 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189517 | |
| dc.description.abstractEn | Assuming the Generalized Riemann Hypothesis, Bach has shown that one can calculate the residue of the Dedekind zeta function of a number field K by a clever use of the splitting of primes p < X, with an error asymptotically bounded by 8.33 log D_K/(\sqrt{X}\log X), where D_K is the absolute value of the discriminant of K. Guided by Weil's explicit formula and still assuming GRH, we make a different use of the splitting of primes and thereby improve Bach's constant to 2.33. This results in substantial speeding of one part of Buchmann's class group algorithm. | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.title.en | Computing the residue of the Dedekind zeta function | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1090/S0025-5718-2014-02843-3 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1305.0035 | |
| dc.description.sponsorshipEurope | Algorithmic Number Theory in Computer Science | |
| bordeaux.journal | Mathematics of Computation | |
| bordeaux.page | 357-369 | |
| bordeaux.volume | 84 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 291 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00916654 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00916654v1 | |
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