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arXiv · 1910.08274

Explicit zero density estimate for the Riemann zeta-function near the critical line

Aleksander Simonič
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Abstract

In 1946, A. Selberg proved $N(\sigma,T) \ll T^{1-\frac{1}{4} \left(\sigma-\frac{1}{2}\right)} \log{T}$ where $N(\sigma,T)$ is the number of nontrivial zeros $\rho$ of the Riemann zeta-function with $\Re\{\rho\}>\sigma$ and $0<\Im\{\rho\}\leq T$. We provide an explicit version of this estimate, together with an explicit approximate functional equation and an explicit upper bound for the second power moment of the zeta-function on the critical line.

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Aleksander Simonič. 2019-10-18. Explicit zero density estimate for the Riemann zeta-function near the critical line. https://arxiv.org/abs/1910.08274

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