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Identitites for Field Extensions Generalizing the Ohno–Nakagawa Relations

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
dc.contributor.authorCOHEN, Henri
hal.structure.identifierDepartment of Statistics [Stanford]
dc.contributor.authorRUBINSTEIN-SALZEDO, Simon
hal.structure.identifierDepartment of Mathematics [Columbia]
dc.contributor.authorTHORNE, Frank
dc.date.accessioned2024-04-04T03:19:11Z
dc.date.available2024-04-04T03:19:11Z
dc.date.created2015
dc.date.issued2015
dc.identifier.issn0010-437X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194482
dc.description.abstractEnIn previous work, Ohno [Ohn97] conjectured, and Nakagawa [Nak98] proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them as consequences of 'extra functional equations' involving the Shintani zeta functions associated to the prehomogeneous vector space of binary cubic forms. In the present paper we generalize their result by proving a similar identity relating certain degree fields with Galois groups D and F respectively, for any odd prime, and in particular we give another proof of the Ohno–Nakagawa relation without appealing to binary cubic forms.
dc.language.isoen
dc.publisherFoundation Compositio Mathematica
dc.title.enIdentitites for Field Extensions Generalizing the Ohno–Nakagawa Relations
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.description.sponsorshipEuropeAlgorithmic Number Theory in Computer Science
bordeaux.journalCompositio Mathematica
bordeaux.page2059-2075
bordeaux.volume151
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue11
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01109980
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01109980v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Compositio%20Mathematica&rft.date=2015&rft.volume=151&rft.issue=11&rft.spage=2059-2075&rft.epage=2059-2075&rft.eissn=0010-437X&rft.issn=0010-437X&rft.au=COHEN,%20Henri&RUBINSTEIN-SALZEDO,%20Simon&THORNE,%20Frank&rft.genre=article


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