Geodesic
On the distribution of $(k,r)$-integers in Piatetski-Shapiro sequences
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1063-1070.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A natural number $n$ is said to be a $(k,r)$-integer if $n=a^kb$, where $k>r>1$ and $b$ is not divisible by the $r$th power of any prime. We study the distribution of such $(k,r)$-integers in the Piatetski-Shapiro sequence $\{\lfloor n^c \rfloor \}$ with $c>1$. As a corollary, we also obtain similar results for semi-$r$-free integers.
DOI : 10.21136/CMJ.2021.0194-20
Classification : 11L07, 11N37
Keywords: $(k, r)$-integer; Piatetski-Shapiro sequence 
@article{10_21136_CMJ_2021_0194_20,
     author = {Srichan, Teerapat},
     title = {On the distribution of $(k,r)$-integers  in {Piatetski-Shapiro} sequences},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1063--1070},
     publisher = {mathdoc},
     volume = {71},
     number = {4},
     year = {2021},
     doi = {10.21136/CMJ.2021.0194-20},
     mrnumber = {4339111},
     zbl = {07442474},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0194-20/}
}
TY  - JOUR
AU  - Srichan, Teerapat
TI  - On the distribution of $(k,r)$-integers  in Piatetski-Shapiro sequences
JO  - Czechoslovak Mathematical Journal
PY  - 2021
SP  - 1063
EP  - 1070
VL  - 71
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0194-20/
DO  - 10.21136/CMJ.2021.0194-20
LA  - en
ID  - 10_21136_CMJ_2021_0194_20
ER  - 
%0 Journal Article
%A Srichan, Teerapat
%T On the distribution of $(k,r)$-integers  in Piatetski-Shapiro sequences
%J Czechoslovak Mathematical Journal
%D 2021
%P 1063-1070
%V 71
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0194-20/
%R 10.21136/CMJ.2021.0194-20
%G en
%F 10_21136_CMJ_2021_0194_20
Srichan, Teerapat. On the distribution of $(k,r)$-integers  in Piatetski-Shapiro sequences. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1063-1070. doi : 10.21136/CMJ.2021.0194-20. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0194-20/

Cité par Sources :