= Vinogradov-Korobov zero-free region
{c}
{title2=$\sigma\ge1-c(\log|t|)^{-2/3}(\log\log|t|)^{-1/3}$}
For sufficiently large $|t|$, the <Riemann zeta function> has no zeros in the displayed region, for a fixed positive $c$. To derive it from the <Richert bound for the Riemann zeta function>, take $\eta\asymp(\log\log t/\log t)^{2/3}$. The logarithm of the maximum on the two discs in the <Landau zero-free-region theorem> is $O(\log\log t)$, as is $\log(1/\eta)$. Dividing $\eta$ by this logarithmic factor gives the displayed width.
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