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Mean-periodicity and zeta functions

dc.contributor.authorSUZUKI, Masatoshi
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorRICOTTA, Guillaume
dc.contributor.authorFESENKO, Ivan
dc.date.accessioned2024-04-04T03:21:43Z
dc.date.available2024-04-04T03:21:43Z
dc.date.created2008-11-08
dc.date.issued2012
dc.identifier.issn0373-0956
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194682
dc.description.abstractEnThis paper establishes new bridges between number theory and modern harmonic analysis, namely between the class of complex functions, which contains zeta functions of arithmetic schemes and closed with respect to product and quotient, and the class of mean-periodic functions in several spaces of functions on the real line. In particular, the meromorphic continuation and functional equation of the zeta function of arithmetic scheme with its expected analytic shape is shown to correspond to mean-periodicity of a certain explicitly defined function associated to the zeta function. This correspondence can be viewed as an extension of the Hecke--Weil correspondence. The case of elliptic curves over number fields and their regular models is treated in more details, and many other examples are included as well.
dc.language.isoen
dc.publisherAssociation des Annales de l'Institut Fourier
dc.title.enMean-periodicity and zeta functions
dc.typeArticle de revue
dc.identifier.doi10.5802/aif.2737
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.identifier.arxiv0803.2821
bordeaux.journalAnnales de l'Institut Fourier
bordeaux.page1819-1887
bordeaux.volume62
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue5
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01023573
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01023573v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annales%20de%20l'Institut%20Fourier&rft.date=2012&rft.volume=62&rft.issue=5&rft.spage=1819-1887&rft.epage=1819-1887&rft.eissn=0373-0956&rft.issn=0373-0956&rft.au=SUZUKI,%20Masatoshi&RICOTTA,%20Guillaume&FESENKO,%20Ivan&rft.genre=article


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