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

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 $0<\Im \{\rho \}\le T$. 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.

35 pages, 1 figure, 3 tables