Sum of the triple divisor function of mixed powers
Let $ d_3(n) $ denote the 3-th divisor function. In this paper, we study the asymptotic formula of the sum $ \sum\limits_{\substack{1 \leqslant n_1,n_2 \leqslant X^{\frac{1}{2}} \\ 1 \leqslant n_3 \leqslant X^{\frac{1}{k}}}} d_3(n_1^2+n_2^2+n_3^k) $ with $ n_1, n_2, n_3\in \mathbb{Z}^+ $...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022713?viewType=HTML |
| _version_ | 1828793353599188992 |
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| author | Li Zhou Liqun Hu |
| author_facet | Li Zhou Liqun Hu |
| author_sort | Li Zhou |
| collection | DOAJ |
| description | Let $ d_3(n) $ denote the 3-th divisor function. In this paper, we study the asymptotic formula of the sum
$ \sum\limits_{\substack{1 \leqslant n_1,n_2 \leqslant X^{\frac{1}{2}} \\ 1 \leqslant n_3 \leqslant X^{\frac{1}{k}}}} d_3(n_1^2+n_2^2+n_3^k) $
with $ n_1, n_2, n_3\in \mathbb{Z}^+ $ and $ k \geqslant 3 $ be an integer. Previously only the case of $ k=2 $ is studied. |
| first_indexed | 2024-12-12T03:25:07Z |
| format | Article |
| id | doaj.art-89ccd7d84d4f48b78fe38493fa1514fb |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-12T03:25:07Z |
| publishDate | 2022-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-89ccd7d84d4f48b78fe38493fa1514fb2022-12-22T00:40:04ZengAIMS PressAIMS Mathematics2473-69882022-05-0177128851289610.3934/math.2022713Sum of the triple divisor function of mixed powersLi Zhou0Liqun Hu11. Department of Mathematics, Nanchang University, Nanchang 330031, Jiangxi, China1. Department of Mathematics, Nanchang University, Nanchang 330031, Jiangxi, China 2. Institute of Mathematics and Interdisciplinary Sciences, Nanchang University, Nanchang 330031, Jiangxi, ChinaLet $ d_3(n) $ denote the 3-th divisor function. In this paper, we study the asymptotic formula of the sum $ \sum\limits_{\substack{1 \leqslant n_1,n_2 \leqslant X^{\frac{1}{2}} \\ 1 \leqslant n_3 \leqslant X^{\frac{1}{k}}}} d_3(n_1^2+n_2^2+n_3^k) $ with $ n_1, n_2, n_3\in \mathbb{Z}^+ $ and $ k \geqslant 3 $ be an integer. Previously only the case of $ k=2 $ is studied.https://www.aimspress.com/article/doi/10.3934/math.2022713?viewType=HTMLcircle methoddivisor problemasymptotic formulamixed powers |
| spellingShingle | Li Zhou Liqun Hu Sum of the triple divisor function of mixed powers AIMS Mathematics circle method divisor problem asymptotic formula mixed powers |
| title | Sum of the triple divisor function of mixed powers |
| title_full | Sum of the triple divisor function of mixed powers |
| title_fullStr | Sum of the triple divisor function of mixed powers |
| title_full_unstemmed | Sum of the triple divisor function of mixed powers |
| title_short | Sum of the triple divisor function of mixed powers |
| title_sort | sum of the triple divisor function of mixed powers |
| topic | circle method divisor problem asymptotic formula mixed powers |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022713?viewType=HTML |
| work_keys_str_mv | AT lizhou sumofthetripledivisorfunctionofmixedpowers AT liqunhu sumofthetripledivisorfunctionofmixedpowers |