Derivation of an actual bound for zeros of Riemann's zeta function by Hadamard's method (Q1358335)

The purpose of this note is to prove the following explicit form of the sharpest known zero-free region for the Riemann zeta-function \(\zeta(s)\) [see for example Chapter 6 of the reviewer's monograph ``The Riemann zeta-function'', John Wiley \& Sons (1985; Zbl 0556.10026)]: \(\zeta(\sigma+it) \not= 0\) for \[ \sigma \geq 1 - {\textstyle{1\over B}} (\log(|t|+10))^{-2/3}(\log\log(|t|+10))^{-1/3}, \quad B = 0,000068880. \] The merit of such a result is in the explicit value of the constant \(B\).