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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
dc.contributor.authorBELABAS, Karim
hal.structure.identifierUniversidad de Santiago de Chile [Santiago] [USACH]
dc.contributor.authorFRIEDMAN, Eduardo
dc.date.accessioned2024-04-04T02:20:44Z
dc.date.available2024-04-04T02:20:44Z
dc.date.created2013-04-30
dc.date.issued2015
dc.identifier.issn0025-5718
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189517
dc.description.abstractEnAssuming 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.isoen
dc.publisherAmerican Mathematical Society
dc.title.enComputing the residue of the Dedekind zeta function
dc.typeArticle de revue
dc.identifier.doi10.1090/S0025-5718-2014-02843-3
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.identifier.arxiv1305.0035
dc.description.sponsorshipEuropeAlgorithmic Number Theory in Computer Science
bordeaux.journalMathematics of Computation
bordeaux.page357-369
bordeaux.volume84
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue291
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00916654
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00916654v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Mathematics%20of%20Computation&amp;rft.date=2015&amp;rft.volume=84&amp;rft.issue=291&amp;rft.spage=357-369&amp;rft.epage=357-369&amp;rft.eissn=0025-5718&amp;rft.issn=0025-5718&amp;rft.au=BELABAS,%20Karim&amp;FRIEDMAN,%20Eduardo&amp;rft.genre=article


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