On the error term in the explicit formula of Riemann--von Mangoldt
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866910288528277504 |
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| author | Cully-Hugill, Michaela Johnston, Daniel R. |
| author_facet | Cully-Hugill, Michaela Johnston, Daniel R. |
| contents | We provide an explicit $O(x\log x/T)$ error term for the Riemann--von Mangoldt formula by making results of Wolke (1983) and Ramaré (2016) explicit. We also include applications to primes between consecutive powers, the error term in the prime number theorem and an inequality of Ramanujan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_10001 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the error term in the explicit formula of Riemann--von Mangoldt Cully-Hugill, Michaela Johnston, Daniel R. Number Theory 11M26 (Primary) 11N05, 11Y70 (Secondary) We provide an explicit $O(x\log x/T)$ error term for the Riemann--von Mangoldt formula by making results of Wolke (1983) and Ramaré (2016) explicit. We also include applications to primes between consecutive powers, the error term in the prime number theorem and an inequality of Ramanujan. |
| title | On the error term in the explicit formula of Riemann--von Mangoldt |
| topic | Number Theory 11M26 (Primary) 11N05, 11Y70 (Secondary) |
| url | https://arxiv.org/abs/2111.10001 |