J. Korean Math. Soc. 2014; 51(6): 1291-1304
Printed November 1, 2014
https://doi.org/10.4134/JKMS.2014.51.6.1291
Copyright © The Korean Mathematical Society.
Woo-Jin Jang and Soun-Hi Kwon
Korea University, Korea University
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
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