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

We will provide the first explicit log-free zero-density estimate for ζ(s) of the form N(σ,T)≤ ATB(1-σ). In particular, this estimate becomes the sharpest known explicit zero-density estimate uniformly for σ∈[α₀,1], with 0.985≤ α₀≤ 0.992 and 3· 10¹²<T≤ exp(6.7· 10¹²).