Zero-free regions for the Riemann zeta function
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866915155723419648 |
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| author | Ford, Kevin |
| author_facet | Ford, Kevin |
| contents | We improve existing explicit bounds of Vinogradov-Korobov type for zero-free regions of the Riemann zeta function, both for large height t and for every t. A primary input is an explicit bound of the author (Proc. London Math. Soc. 85 (2002), 565-633) for the growth of $ζ(σ+it)$ for $σ$ near 1. Another ingredient is a kind of Jensen formula (Lemma 2.2) relating the growth of a function on vertical lines to a weighted count of its zeros inside a vertical strip. The latter was used recently in the weak subconvexity work of Soundararajan and Thorner (arXiv:1804.03654, Duke Math. J. 168, no. 7 (2019), 1231-1268). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_08205 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Zero-free regions for the Riemann zeta function Ford, Kevin Number Theory We improve existing explicit bounds of Vinogradov-Korobov type for zero-free regions of the Riemann zeta function, both for large height t and for every t. A primary input is an explicit bound of the author (Proc. London Math. Soc. 85 (2002), 565-633) for the growth of $ζ(σ+it)$ for $σ$ near 1. Another ingredient is a kind of Jensen formula (Lemma 2.2) relating the growth of a function on vertical lines to a weighted count of its zeros inside a vertical strip. The latter was used recently in the weak subconvexity work of Soundararajan and Thorner (arXiv:1804.03654, Duke Math. J. 168, no. 7 (2019), 1231-1268). |
| title | Zero-free regions for the Riemann zeta function |
| topic | Number Theory |
| url | https://arxiv.org/abs/1910.08205 |