| Title:
|
On generalized square-full numbers in an arithmetic progression (English) |
| Author:
|
Sripayap, Angkana |
| Author:
|
Ruengsinsub, Pattira |
| Author:
|
Srichan, Teerapat |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
72 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
149-163 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\alpha _i$ $(1\leq i\leq r)$ being a multiple of $a$ or belonging to the arithmetic progression $at+b$, $t\in \mathbb {N}_0:=\mathbb {N}\cup \{0\}$. 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. (English) |
| Keyword:
|
arithmetic progression |
| Keyword:
|
character sum |
| Keyword:
|
exponent pair method |
| Keyword:
|
square-full number |
| MSC:
|
11B50 |
| MSC:
|
11N25 |
| MSC:
|
11N69 |
| idZBL:
|
Zbl 07511558 |
| idMR:
|
MR4389111 |
| DOI:
|
10.21136/CMJ.2021.0362-20 |
| . |
| Date available:
|
2022-03-25T08:28:27Z |
| Last updated:
|
2024-04-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149578 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
|
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| . |
