Randomness and non-randomness properties of Piatetski-Shapiro sequences modulo m
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DESHOUILLERS, Jean-Marc | |
| hal.structure.identifier | Vienna University of Technology = Technische Universität Wien [TU Wien] | |
| dc.contributor.author | DRMOTA, Michael | |
| hal.structure.identifier | Combinatoire, théorie des nombres [CTN] | |
| dc.contributor.author | MÜLLNER, Clemens | |
| hal.structure.identifier | Institut für Diskrete Mathematik und Geometrie [Wien] | |
| dc.contributor.author | SPIEGELHOFFER, Lukas | |
| dc.date.accessioned | 2024-04-04T02:56:57Z | |
| dc.date.available | 2024-04-04T02:56:57Z | |
| dc.date.issued | 2019 | |
| dc.identifier.issn | 0025-5793 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192514 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.publisher | University College London | |
| dc.title.en | Randomness and non-randomness properties of Piatetski-Shapiro sequences modulo m | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1112/S0025579319000287 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| bordeaux.journal | Mathematika | |
| bordeaux.page | 1051-1073 | |
| bordeaux.volume | 65 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02480007 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02480007v1 | |
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