Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.13666 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913472982286336 |
|---|---|
| author | Du, Chenhao Sun, Qingfeng |
| author_facet | Du, Chenhao Sun, Qingfeng |
| contents | Let $τ_k(n)$ be the $k$-th divisor function. In this paper, we derive an asymptotic formula for the sum $$ \sum_{1\leq n_1,n_2, \dots, n_{\ell}\leq X^{\frac{1}{r}} \atop 1\leq n_{\ell+1}\le X^{\frac{1}{s}}}τ_k(n_1^r+n_2^r+\dots +n_{\ell}^r+n_{\ell+1}^s), $$ where $k\geq 4$, $r\geq 2$, $s\geq 2$ and $\ell\geq 2$ are integers. Previously only special cases are studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher order divisor functions over values of mixed powers Du, Chenhao Sun, Qingfeng Number Theory Let $τ_k(n)$ be the $k$-th divisor function. In this paper, we derive an asymptotic formula for the sum $$ \sum_{1\leq n_1,n_2, \dots, n_{\ell}\leq X^{\frac{1}{r}} \atop 1\leq n_{\ell+1}\le X^{\frac{1}{s}}}τ_k(n_1^r+n_2^r+\dots +n_{\ell}^r+n_{\ell+1}^s), $$ where $k\geq 4$, $r\geq 2$, $s\geq 2$ and $\ell\geq 2$ are integers. Previously only special cases are studied. |
| title | Higher order divisor functions over values of mixed powers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.13666 |