Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.10119 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910140468297728 |
|---|---|
| author | Zhang, Wei |
| author_facet | Zhang, Wei |
| contents | In this paper, we consider the general divisor functions over Piatetski-Shapiro sequences. We can give some general results which contain some special divisor functions. Precisely, we extend the divisor problem over Piatetski-Shapiro sequences to the function $f(n),$ where $f(n)\ll n^{\varepsilon},$ $$f(n)=\sum_{n=n_{1}n_{2}} τ(n_{1})g(n_{2}),$$ $τ(n)$ is the number of representations of $n$ as product of two natural numbers
and \[ \sum_{1\leq n\leq x}|g(n)|\ll x^{5/8+\varepsilon}. \] On the other hand, we also considered these arithmetic functions over Piatetski-Shapiro sequences in arithmetic progressions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10119 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On general divisor functions over Piatetski-Shapiro sequences Zhang, Wei Number Theory In this paper, we consider the general divisor functions over Piatetski-Shapiro sequences. We can give some general results which contain some special divisor functions. Precisely, we extend the divisor problem over Piatetski-Shapiro sequences to the function $f(n),$ where $f(n)\ll n^{\varepsilon},$ $$f(n)=\sum_{n=n_{1}n_{2}} τ(n_{1})g(n_{2}),$$ $τ(n)$ is the number of representations of $n$ as product of two natural numbers and \[ \sum_{1\leq n\leq x}|g(n)|\ll x^{5/8+\varepsilon}. \] On the other hand, we also considered these arithmetic functions over Piatetski-Shapiro sequences in arithmetic progressions. |
| title | On general divisor functions over Piatetski-Shapiro sequences |
| topic | Number Theory |
| url | https://arxiv.org/abs/2304.10119 |