A zero density result for the Riemann zeta function

Abstract

In this article, we prove an explicit bound for $N(\sigma ,T)$, the number of zeros of the Riemann zeta function satisfying $\sigma <\Re s<1$ and $0<\Im s<T$. This result provides a significant improvement over Rosser's bound for $N(T)$ when used for estimating prime counting functions. For instance this is applied to obtain new bounds for $\psi (x)$ (arXiv:1310.6374).

arXiv comment15 pages