Journal of the
Korean Mathematical Society JKMS

In 2005 Kadiri proved that the Riemann zeta function $\zeta(s)$ does not vanish in the region $${\rm Re}(s) \geq 1 - \frac{1}{R_0 \log | {\rm Im}(s) |},~~~| {\rm Im}(s) | \geq 2$$ 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.

Keywords: Riemann zeta function, zero-free regions, Riemann Hypothesis

MSC numbers: Primary 11M06, 11M26; Secondary 11Y35