On the distribution of -integers in Piatetski-Shapiro sequences
Czechoslovak Mathematical Journal (2021)
- Volume: 71, Issue: 4, page 1063-1070
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topSrichan, Teerapat. "On the distribution of $(k,r)$-integers in Piatetski-Shapiro sequences." Czechoslovak Mathematical Journal 71.4 (2021): 1063-1070. <http://eudml.org/doc/298107>.
@article{Srichan2021,
abstract = {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 $\lbrace \lfloor n^c \rfloor \rbrace $ with $c>1$. As a corollary, we also obtain similar results for semi-$r$-free integers.},
author = {Srichan, Teerapat},
journal = {Czechoslovak Mathematical Journal},
keywords = {$(k,r)$-integer; Piatetski-Shapiro sequence},
language = {eng},
number = {4},
pages = {1063-1070},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the distribution of $(k,r)$-integers in Piatetski-Shapiro sequences},
url = {http://eudml.org/doc/298107},
volume = {71},
year = {2021},
}
TY - JOUR
AU - Srichan, Teerapat
TI - On the distribution of $(k,r)$-integers in Piatetski-Shapiro sequences
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 4
SP - 1063
EP - 1070
AB - 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 $\lbrace \lfloor n^c \rfloor \rbrace $ with $c>1$. As a corollary, we also obtain similar results for semi-$r$-free integers.
LA - eng
KW - $(k,r)$-integer; Piatetski-Shapiro sequence
UR - http://eudml.org/doc/298107
ER -
References
top- Cao, X., Zhai, W., 10.5802/jtnb.229, J. Théor. Nombres Bordx. 10 (1998), 287-299. (1998) Zbl0926.11066MR1828246DOI10.5802/jtnb.229
- Cao, X., Zhai, W., On the distribution of square-free numbers of the form . II, Acta Math. Sin., Chin. Ser. 51 (2008), 1187-1194 Chinese. (2008) Zbl1174.11395MR2490038
- Deshouillers, J.-M., A remark on cube-free numbers in Segal-Piatetski-Shapiro sequences, Hardy-Ramanujan J. 41 (2018), 127-132. (2018) Zbl1448.11055MR3935505
- Ivić, A., The Riemann Zeta-Function: The Theory of the Riemann Zeta-Function, A Wiley-Interscience Publication. John Wiley & Sons, New York (1985). (1985) Zbl0556.10026MR792089
- Piatetski-Shapiro, I. I., On the distribution of prime numbers in sequences of the form , Mat. Sb., N.Ser. 33 (1953), 559-566 Russian. (1953) Zbl0053.02702MR0059302
- Rieger, G. J., 10.2140/pjm.1978.78.241, Pac. J. Math. 78 (1978), 241-242. (1978) Zbl0395.10049MR513296DOI10.2140/pjm.1978.78.241
- Stux, I. E., 10.2140/pjm.1975.59.577, Pac. J. Math. 59 (1975), 577-584. (1975) Zbl0297.10033MR387218DOI10.2140/pjm.1975.59.577
- Subbarao, M. V., Suryanarayana, D., 10.1016/0022-314X(74)90049-3, J. Number Theory 6 (1974), 112-123. (1974) Zbl0277.10036MR0335454DOI10.1016/0022-314X(74)90049-3
- Zhang, M., Li, J., 10.1007/s11464-017-0652-1, Front. Math. China 12 (2017), 1515-1525. (2017) Zbl1418.11137MR3722230DOI10.1007/s11464-017-0652-1
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.