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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.00936 |
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| _version_ | 1866929523600130048 |
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| author | Guo, Zhen Li, Xin |
| author_facet | Guo, Zhen Li, Xin |
| contents | Let $3\leqslant k\leqslant9$ be a fixed integer, $p$ be a prime and $d(n)$ denote the Dirichlet divisor function. We use $Δ(x)$ to denote the error term in the asymptotic formula of the summatory function of $d(n)$. The aim of this paper is to study the $k$-th power moments of $Δ(p)$, namely $\sum_{p\leqslant x}Δ^k(p)$, and we give an asymptotic formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00936 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On high power moments of the error term of the Dirichlet divisor function over primes Guo, Zhen Li, Xin Number Theory Let $3\leqslant k\leqslant9$ be a fixed integer, $p$ be a prime and $d(n)$ denote the Dirichlet divisor function. We use $Δ(x)$ to denote the error term in the asymptotic formula of the summatory function of $d(n)$. The aim of this paper is to study the $k$-th power moments of $Δ(p)$, namely $\sum_{p\leqslant x}Δ^k(p)$, and we give an asymptotic formula. |
| title | On high power moments of the error term of the Dirichlet divisor function over primes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.00936 |