On large values of the Riemann zeta-function on short segments of the critical line
Volume 166 / 2014
Acta Arithmetica 166 (2014), 349-390
MSC: Primary 11M06.
DOI: 10.4064/aa166-4-3
Abstract
We obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based on the Riemann hypothesis. In particular, we prove that for any large fixed constant $A>1$ there exist (non-effective) constants $T_{0}(A)>0$ and $c_{0}(A)>0$ such that the maximum of $|\zeta (0.5+it)|$ on the interval $(T-h,T+h)$ is greater than $A$ for any $T>T_{0}$ and $h = (1/\pi)\ln\ln\ln{T}+c_{0}$.
