Journal of the Korean Mathematical Society (대한수학회지)

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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)
  • Received : 2014.03.14
  • Published : 2014.11.01
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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.

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References

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