A remark on cube-free numbers in Segal-Piatestki-Shapiro sequences
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DESHOUILLERS, Jean-Marc | |
| dc.date.accessioned | 2024-04-04T03:02:21Z | |
| dc.date.available | 2024-04-04T03:02:21Z | |
| dc.date.issued | 2019-01-23 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192975 | |
| dc.description.abstractEn | Using a method due to G. J. Rieger, we show that for $1 < c < 2 $ one has, as $x$ tends to infinity $$\textrm{Card}{n \leq x : \lfloor{n^c}\rfloor} \ \textrm{ is cube-free} } = \frac{x}{\zeta(3)} + O (x^{ (c+1)/3} \log x)$$ , thus improving on a recent result by Zhang Min and Li Jinjiang. | |
| dc.language.iso | en | |
| dc.publisher | Hardy-Ramanujan Society | |
| dc.subject.en | Segal-Piatetski-Shapiro sequences | |
| dc.subject.en | cube-free numbers | |
| dc.subject.en | estimation of trigonometric sums | |
| dc.subject.en | discrepancy 2010 Mathematics Subject Classification 11B75 | |
| dc.subject.en | 11N37 | |
| dc.subject.en | 11N56 | |
| dc.subject.en | 11L03 | |
| dc.subject.en | 11L07 | |
| dc.title.en | A remark on cube-free numbers in Segal-Piatestki-Shapiro sequences | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.46298/hrj.2019.5114 | |
| dc.subject.hal | Mathématiques [math] | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| bordeaux.journal | Hardy-Ramanujan Journal | |
| bordeaux.page | 127 - 132 | |
| bordeaux.volume | Atelier Digit_Hum | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01986712 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01986712v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Hardy-Ramanujan%20Journal&rft.date=2019-01-23&rft.volume=Atelier%20Digit_Hum&rft.spage=127%20-%20132&rft.epage=127%20-%20132&rft.au=DESHOUILLERS,%20Jean-Marc&rft.genre=article |
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