A remark on cube-free numbers in Segal-Piatestki-Shapiro sequences - Archive ouverte HAL Access content directly
Journal Articles Hardy-Ramanujan Journal Year : 2019

A remark on cube-free numbers in Segal-Piatestki-Shapiro sequences

Abstract

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.
Fichier principal
Vignette du fichier
41Article14.pdf (245.23 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01986712 , version 1 (19-01-2019)

Identifiers

Cite

Jean-Marc Deshouillers. A remark on cube-free numbers in Segal-Piatestki-Shapiro sequences. Hardy-Ramanujan Journal, 2019, Atelier Digit_Hum, pp.127 - 132. ⟨10.46298/hrj.2019.5114⟩. ⟨hal-01986712⟩

Collections

CNRS INSMI
47 View
577 Download

Altmetric

Share

Gmail Facebook X LinkedIn More