On the error in the prime number theorem in short intervals
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912674359541760 |
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| author | Lee, Ethan Simpson |
| author_facet | Lee, Ethan Simpson |
| contents | Assuming the Riemann Hypothesis, we derive explicit bounds for the error terms in short interval analogues of the prime number theorem and Mertens' theorems using a smoothing argument. Our results improve upon previous bounds in both constant terms and applicable ranges, notably improving and extending earlier work by Cully-Hugill and Dudek. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11814 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the error in the prime number theorem in short intervals Lee, Ethan Simpson Number Theory 11N05, 11L20, 11Y35, 11M26, 11M06 Assuming the Riemann Hypothesis, we derive explicit bounds for the error terms in short interval analogues of the prime number theorem and Mertens' theorems using a smoothing argument. Our results improve upon previous bounds in both constant terms and applicable ranges, notably improving and extending earlier work by Cully-Hugill and Dudek. |
| title | On the error in the prime number theorem in short intervals |
| topic | Number Theory 11N05, 11L20, 11Y35, 11M26, 11M06 |
| url | https://arxiv.org/abs/2403.11814 |