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http://dx.doi.org/10.4134/JKMS.2014.51.6.1291

A NOTE ON KADIRI'S EXPLICIT ZERO FREE REGION FOR RIEMANN ZETA FUNCTION  

Jang, Woo-Jin (Department of Mathematics Korea University)
Kwon, Soun-Hi (Department of Mathematics Education Korea University)
Publication Information
Journal of the Korean Mathematical Society / v.51, no.6, 2014 , pp. 1291-1304 More about this Journal
Abstract
In 2005 Kadiri proved that the Riemann zeta function ${\zeta}(s)$ does not vanish in the region $$Re(s){\geq}1-\frac{1}{R_0\;{\log}\;{\mid}Im(s){\mid}},\;{\mid}Im(s){\mid}{\geq}2$$ 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;
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