A zero density result for the Riemann zeta function

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

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