An explicit log-free zero density estimate for the Riemann zeta-function
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909210269188096 |
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| author | Bellotti, Chiara |
| author_facet | Bellotti, Chiara |
| contents | We will provide an explicit log-free zero-density estimate for $ζ(s)$ of the form $N(σ,T)\le AT^{B(1-σ)}$. In particular, this estimate becomes the sharpest known explicit zero-density estimate uniformly for $σ\in[α_0,1]$, with $0.985\le α_0\le 0.9927$ and $3\cdot 10^{12}<T\le \exp(6.7\cdot 10^{12})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12545 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An explicit log-free zero density estimate for the Riemann zeta-function Bellotti, Chiara Number Theory Primary 11M06, 11M26. Secondary 11Y35 We will provide an explicit log-free zero-density estimate for $ζ(s)$ of the form $N(σ,T)\le AT^{B(1-σ)}$. In particular, this estimate becomes the sharpest known explicit zero-density estimate uniformly for $σ\in[α_0,1]$, with $0.985\le α_0\le 0.9927$ and $3\cdot 10^{12}<T\le \exp(6.7\cdot 10^{12})$. |
| title | An explicit log-free zero density estimate for the Riemann zeta-function |
| topic | Number Theory Primary 11M06, 11M26. Secondary 11Y35 |
| url | https://arxiv.org/abs/2405.12545 |