Geodesic
Squarefree numbers in the sequence $[\alpha n]$
Čebyševskij sbornik, Tome 14 (2013) no. 3, pp. 42-48 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An asymptotic formula for the number of squarefree integers of the form $[\alpha n]$ is proved in the paper, where $\alpha$ is an algebraic number or a number with restricted partial quotients.
Keywords: squarefree numbers, Beatty sequence, asymptotic formula, exponential sums. 
@article{CHEB_2013_14_3_a4,
     author = {D. V. Goryashin},
     title = {Squarefree numbers in the sequence $[\alpha n]$},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {42--48},
     year = {2013},
     volume = {14},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2013_14_3_a4/}
}
TY  - JOUR
AU  - D. V. Goryashin
TI  - Squarefree numbers in the sequence $[\alpha n]$
JO  - Čebyševskij sbornik
PY  - 2013
SP  - 42
EP  - 48
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CHEB_2013_14_3_a4/
LA  - ru
ID  - CHEB_2013_14_3_a4
ER  - 
%0 Journal Article
%A D. V. Goryashin
%T Squarefree numbers in the sequence $[\alpha n]$
%J Čebyševskij sbornik
%D 2013
%P 42-48
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/CHEB_2013_14_3_a4/
%G ru
%F CHEB_2013_14_3_a4
D. V. Goryashin. Squarefree numbers in the sequence $[\alpha n]$. Čebyševskij sbornik, Tome 14 (2013) no. 3, pp. 42-48. http://geodesic.mathdoc.fr/item/CHEB_2013_14_3_a4/

[1] Güloğlu A. M., Nevans C. W., “Sums of multiplicative functions over a Beatty sequence”, Bull. Austral. Math. Soc., 78 (2008), 327—334 | DOI | MR | Zbl

[2] Abercrombie A. G., Banks W. D., Shparlinski I. E., “Arithmetic functions on Beatty sequences”, Acta Arith., 136:1 (2009), 81—89 | DOI | MR | Zbl

[3] Arkhipov G. I., Sadovnichii V. A., Chubarikov V. N., Lektsii po matematicheskomu analizu, 3-e izd., pererab. i dop., Drofa, M., 2003