A note on Kadiri's explicit zero free region for Riemann zeta function

摘要

In 2005 Kadiri proved that the Riemann zeta function $zeta(s)$ does not vanish in the region $${m Re}(s) geq 1 - rac{1}{R_0 log | {m Im}(s) |},~~~| {m Im}(s) | geq 2$$ with $R_0=5.69693$. In this paper we will show that $R_0$ can be taken $R_0=5.68371$ using Kadiri's method together with Platt's numerical verification of Riemann Hypothesis.