Explicit zero density estimate for the Riemann zeta-function near the critical line (1910.08274v2)

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.