An explicit version of Carlson's theorem

Let $N(\sigma ,T)$ denote the number of nontrivial zeros of the Riemann zeta function with real part greater than $\sigma$ and imaginary part lying between $0$ and $T$. In this article, we provide an explicit version of Carlson’s zero density estimate, that is, $N(\sigma ,T)\le 0.78T^{4\sigma (1-\sigma )}(\log T{)}^{5-2\sigma }$, with a slight improvement in the exponent of the logarithm factor.