Zero-free regions inspired by work of Heath-Brown
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914413759430656 |
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| author | Bellotti, Chiara Trudgian, Tim Yang, Andrew |
| author_facet | Bellotti, Chiara Trudgian, Tim Yang, Andrew |
| contents | We prove a new explicit zero-free region for the Riemann zeta-function, drawing substantially on Heath-Brown's seminal work on Linnik's constant. Using these ideas we are able to prove that $ζ(σ+ it)\ne 0$ whenever $t\geq 3$ and $σ\geq 1- 1/(4.896\log t)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21490 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Zero-free regions inspired by work of Heath-Brown Bellotti, Chiara Trudgian, Tim Yang, Andrew Number Theory 11M06, 11M26 We prove a new explicit zero-free region for the Riemann zeta-function, drawing substantially on Heath-Brown's seminal work on Linnik's constant. Using these ideas we are able to prove that $ζ(σ+ it)\ne 0$ whenever $t\geq 3$ and $σ\geq 1- 1/(4.896\log t)$. |
| title | Zero-free regions inspired by work of Heath-Brown |
| topic | Number Theory 11M06, 11M26 |
| url | https://arxiv.org/abs/2603.21490 |