An explicit version of Carlson's theorem
Fuente:
arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916504314839040 |
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| author | Chourasiya, Shashi |
| author_facet | Chourasiya, Shashi |
| contents | Let $N(σ,T)$ denote the number of nontrivial zeros of the Riemann zeta function with real part greater than $σ$ and imaginary part lying between $0$ and $T$. In this article, we provide an explicit version of Carlson's zero density estimate, that is, $N(σ, T) \leq 0.78 T^{4 σ(1- σ)} (\log T)^{5-2 σ} $, with a slight improvement in the exponent of the logarithm factor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An explicit version of Carlson's theorem Chourasiya, Shashi Number Theory 11N56, 11N37 (primary), 11M06 (secondary) Let $N(σ,T)$ denote the number of nontrivial zeros of the Riemann zeta function with real part greater than $σ$ and imaginary part lying between $0$ and $T$. In this article, we provide an explicit version of Carlson's zero density estimate, that is, $N(σ, T) \leq 0.78 T^{4 σ(1- σ)} (\log T)^{5-2 σ} $, with a slight improvement in the exponent of the logarithm factor. |
| title | An explicit version of Carlson's theorem |
| topic | Number Theory 11N56, 11N37 (primary), 11M06 (secondary) |
| url | https://arxiv.org/abs/2412.02068 |