On generalized square-full numbers in an arithmetic progression

Sripayap, Angkana, Ruengsinsub, Pattira, and Srichan, Teerapat. "On generalized square-full numbers in an arithmetic progression." Czechoslovak Mathematical Journal 72.1 (2022): 149-163. <http://eudml.org/doc/297949>.

@article{Sripayap2022,
abstract = {Let $a$ and $b\in \mathbb \{N\}$. Denote by $R_\{a,b\}$ the set of all integers $n>1$ whose canonical prime representation $n=p_1^\{\alpha _1\}p_2^\{\alpha _2\}\cdots p_r^\{\alpha _r\}$ has all exponents $\alpha _i$$(1\le i\le r)$ being a multiple of $a$ or belonging to the arithmetic progression $at+b$, $t\in \mathbb \{N\}_0:=\mathbb \{N\}\cup \lbrace 0\rbrace $. All integers in $R_\{a,b\}$ are called generalized square-full integers. Using the exponent pair method, an upper bound for character sums over generalized square-full integers is derived. An application on the distribution of generalized square-full integers in an arithmetic progression is given.},
author = {Sripayap, Angkana, Ruengsinsub, Pattira, Srichan, Teerapat},
journal = {Czechoslovak Mathematical Journal},
keywords = {arithmetic progression; character sum; exponent pair method; square-full number},
language = {eng},
number = {1},
pages = {149-163},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On generalized square-full numbers in an arithmetic progression},
url = {http://eudml.org/doc/297949},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Sripayap, Angkana
AU - Ruengsinsub, Pattira
AU - Srichan, Teerapat
TI - On generalized square-full numbers in an arithmetic progression
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 1
SP - 149
EP - 163
AB - Let $a$ and $b\in \mathbb {N}$. Denote by $R_{a,b}$ the set of all integers $n>1$ whose canonical prime representation $n=p_1^{\alpha _1}p_2^{\alpha _2}\cdots p_r^{\alpha _r}$ has all exponents $\alpha _i$$(1\le i\le r)$ being a multiple of $a$ or belonging to the arithmetic progression $at+b$, $t\in \mathbb {N}_0:=\mathbb {N}\cup \lbrace 0\rbrace $. All integers in $R_{a,b}$ are called generalized square-full integers. Using the exponent pair method, an upper bound for character sums over generalized square-full integers is derived. An application on the distribution of generalized square-full integers in an arithmetic progression is given.
LA - eng
KW - arithmetic progression; character sum; exponent pair method; square-full number
UR - http://eudml.org/doc/297949
ER -