An explicit version of Carlson's theorem

Abstract

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

10 pages, 1 figure, 1 table