A remark on cube-free numbers in Segal-Piatestki-Shapiro sequences
Langue
en
Article de revue
Ce document a été publié dans
Hardy-Ramanujan Journal. 2019-01-23, vol. Atelier Digit_Hum, p. 127 - 132
Hardy-Ramanujan Society
Résumé en anglais
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 ...Lire la suite >
Mots clés en anglais
Segal-Piatetski-Shapiro sequences
cube-free numbers
estimation of trigonometric sums
discrepancy 2010 Mathematics Subject Classification 11B75
11N37
11N56
11L03
11L07