The Error in a Smooth Weighted Prime Number Formula and Zero-free Regions for the Riemann Zeta Function
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916766928601088 |
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| author | Han, Songlin |
| author_facet | Han, Songlin |
| contents | We study the error bound for a smooth weighted prime number theorem, and its implication to the zero-free region for the Riemann zeta function using the method of Pintz. We also give an application to the average number of smooth weighted Goldbach representations and generalize the result to the case of smooth weighted average k-Goldbach representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Error in a Smooth Weighted Prime Number Formula and Zero-free Regions for the Riemann Zeta Function Han, Songlin Number Theory We study the error bound for a smooth weighted prime number theorem, and its implication to the zero-free region for the Riemann zeta function using the method of Pintz. We also give an application to the average number of smooth weighted Goldbach representations and generalize the result to the case of smooth weighted average k-Goldbach representations. |
| title | The Error in a Smooth Weighted Prime Number Formula and Zero-free Regions for the Riemann Zeta Function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.23795 |