On a variant of the prime number theorem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866916191638913024 |
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| author | Zhang, Wei |
| author_facet | Zhang, Wei |
| contents | In this paper, we can show that \begin{align*} S_Λ(x)=\sum_{1\leq n\leq x}Λ\left(\left[\frac{x}{n}\right]\right)= \sum_{n=1}^{\infty} \frac{Λ(n)}{n(n+1)}x +O\left(x^{7/15+1/195+\varepsilon}\right), \end{align*} where $Λ(n)$ is the von Mangdolt function. Moreover, we can also give a similar result related to the divisor function, which improves previous results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_12347 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On a variant of the prime number theorem Zhang, Wei Number Theory In this paper, we can show that \begin{align*} S_Λ(x)=\sum_{1\leq n\leq x}Λ\left(\left[\frac{x}{n}\right]\right)= \sum_{n=1}^{\infty} \frac{Λ(n)}{n(n+1)}x +O\left(x^{7/15+1/195+\varepsilon}\right), \end{align*} where $Λ(n)$ is the von Mangdolt function. Moreover, we can also give a similar result related to the divisor function, which improves previous results. |
| title | On a variant of the prime number theorem |
| topic | Number Theory |
| url | https://arxiv.org/abs/2303.12347 |