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Dirichlet series associated to cubic fields with given quadratic resolvent

hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCOHEN, Henri
hal.structure.identifierDepartment of Mathematics [Columbia]
dc.contributor.authorTHORNE, Frank
dc.date.accessioned2024-04-04T02:21:41Z
dc.date.available2024-04-04T02:21:41Z
dc.date.created2013-08-14
dc.date.issued2014
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189595
dc.description.abstractEnLet k be a quadratic field. We give an explicit formula for the Dirichlet series enumerating cubic fields whose quadratic resolvent field is isomorphic to k. Our work is a sequel to previous work of Cohen and Morra, where such formulas are proved in a more general setting, in terms of sums over characters of certain groups related to ray class groups. In the present paper we carry the analysis further and prove explicit formulas for these Dirichlet series over Q. In a companion paper we do the same for quartic fields having a given cubic resolvent. As an application (not present in the initial version), we compute tables of the number of S_3-sextic fields E with |Disc(E)| < X, for X ranging up to 10^23. An accompanying PARI/GP implementation is available from the second author's website.
dc.language.isoen
dc.publisherUniversity of Michigan
dc.title.enDirichlet series associated to cubic fields with given quadratic resolvent
dc.typeArticle de revue
dc.identifier.doi10.1307/mmj/1401973050
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.identifier.arxiv1301.3563
dc.description.sponsorshipEuropeAlgorithmic Number Theory in Computer Science
bordeaux.journalMichigan Mathematical Journal
bordeaux.page253-273
bordeaux.volume63
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00854662
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00854662v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Michigan%20Mathematical%20Journal&amp;rft.date=2014&amp;rft.volume=63&amp;rft.spage=253-273&amp;rft.epage=253-273&amp;rft.au=COHEN,%20Henri&amp;THORNE,%20Frank&amp;rft.genre=article


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