An explicit log-free zero density estimate for the Riemann zeta-function

We will provide an explicit log-free zero-density estimate for $\zeta (s)$ of the form $N(\sigma ,T)\le A{T}^{B(1-\sigma )}$. In particular, this estimate becomes the sharpest known explicit zero-density estimate uniformly for $\sigma \in [{\alpha }_0,1]$, with $0.985\le {\alpha }_0\le 0.9927$ and $3\cdot {10}^{12}<T\le \exp (6.7\cdot {10}^{12})$.