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EQUIDISTRIBUTION MODULO 1 AND SALEM NUMBERS

hal.structure.identifierCentre for Advanced Computing - Algorithms and Cryptography [ACAC]
dc.contributor.authorDOCHE, Christophe
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMENDES-FRANCE, Michel
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorRUCH, Jean-Jacques
dc.date.accessioned2024-04-04T02:42:42Z
dc.date.available2024-04-04T02:42:42Z
dc.date.created2007-06-16
dc.date.issued2008-06-16
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191267
dc.description.abstractEnLet θ be a Salem number. It is well-known that the sequence (θ n ) modulo 1 is dense but not equidistributed. In this article we discuss equidistributed subsequences. Our first approach is computational and consists in estimating the supremum of limn→∞ n/s(n) over all equidistributed subsequences (θ s(n) ). As a result, we obtain an explicit upper bound onthe density of any equidistributed subsequence. Our second approach is probabilistic. Defining a measure on the family of increasing integer sequences, we show that relatively to that measure, almost no subsequence is equiditributed.
dc.language.isoen
dc.subject.enSalem number
dc.subject.enEquidistribution modulo 1
dc.subject.enJ0 Bessel function.
dc.subject.enJ0 Bessel function
dc.title.enEQUIDISTRIBUTION MODULO 1 AND SALEM NUMBERS
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
bordeaux.journalFunctiones et Approximatio
bordeaux.page261–271
bordeaux.volumeXXXIX
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00353834
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00353834v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Functiones%20et%20Approximatio&rft.date=2008-06-16&rft.volume=XXXIX&rft.issue=2&rft.spage=261%E2%80%93271&rft.epage=261%E2%80%93271&rft.au=DOCHE,%20Christophe&MENDES-FRANCE,%20Michel&RUCH,%20Jean-Jacques&rft.genre=article


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