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Randomness and non-randomness properties of Piatetski-Shapiro sequences modulo m

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDESHOUILLERS, Jean-Marc
hal.structure.identifierVienna University of Technology = Technische Universität Wien [TU Wien]
dc.contributor.authorDRMOTA, Michael
hal.structure.identifierCombinatoire, théorie des nombres [CTN]
dc.contributor.authorMÜLLNER, Clemens
hal.structure.identifierInstitut für Diskrete Mathematik und Geometrie [Wien]
dc.contributor.authorSPIEGELHOFFER, Lukas
dc.date.accessioned2024-04-04T02:56:57Z
dc.date.available2024-04-04T02:56:57Z
dc.date.issued2019
dc.identifier.issn0025-5793
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192514
dc.description.abstractEnWe study Piatetski-Shapiro sequences ([n(c)])(n) modulo m, for non-integer c > 1 and positive m, and we are particularly interested in subword occurrences in those sequences. We prove that each block is an element of {0, 1}(k) of length k < c + 1 occurs as a subword with the frequency 2(-k), while there are always blocks that do not occur. In particular, those sequences are not normal. For 1 < c < 2, we estimate the number of subwords from above and below, yielding the fact that our sequences are deterministic and not morphic. Finally, using the Daboussi-Katai criterion, we prove that the sequence [n(c)] modulo m is asymptotically orthogonal to multiplicative functions bounded by 1 and with mean value 0.
dc.language.isoen
dc.publisherUniversity College London
dc.title.enRandomness and non-randomness properties of Piatetski-Shapiro sequences modulo m
dc.typeArticle de revue
dc.identifier.doi10.1112/S0025579319000287
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
bordeaux.journalMathematika
bordeaux.page1051-1073
bordeaux.volume65
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02480007
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02480007v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Mathematika&amp;rft.date=2019&amp;rft.volume=65&amp;rft.issue=4&amp;rft.spage=1051-1073&amp;rft.epage=1051-1073&amp;rft.eissn=0025-5793&amp;rft.issn=0025-5793&amp;rft.au=DESHOUILLERS,%20Jean-Marc&amp;DRMOTA,%20Michael&amp;M%C3%9CLLNER,%20Clemens&amp;SPIEGELHOFFER,%20Lukas&amp;rft.genre=article


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