A zero density result for the Riemann zeta function

الأصل · EN

In this article, we prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying σ< s <1 and 0 < 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 ψ(x) (arXiv:1310.6374).