Lower bounds for the large deviations and moments of the Riemann zeta function on the critical line

Abstract

Building on work in \cite{AB24} on the Riemann zeta function at height $T$ off the critical line, we prove an unconditional lower bound on the critical line for real large deviations of the order $V\sim\alpha\log\log T$ for any $\alpha>0.$ This gives another proof of the sharpest known unconditional lower bounds on the fractional moments of the Riemann zeta function, due to \cite{HSlower}. The lower bound on large deviations is of the same order of magnitude as the upper bound proved in \cite{AB23}, for the range $0<\alpha<2.$