Large deviations of the argument of the Riemann zeta function (Q6581854)

Let \N\[\NS(t):=\frac{1}{\pi}\Im\log\zeta\left(\frac{1}{2}+it\right),\N\]\Nwhere \(\zeta\) denotes the Riemmann zeta function and \(\log\zeta(s)\) is defined with a branch that cuts extending horizontally to the left of each zero and pole of the zeta function, and the branch is such that \(\log\zeta(2)\) is real.\N\N\NIn this paper under review, the author proves in the main result (see Theorem 1) an unconditional lower bound on the measure of the sets \(\{t\in{[T,2T]}:\ S(t)\geq V\}\) for \(\sqrt{\log\log T}\leq V\ll\left(\frac{\log T}{\log\log T}\right)^{1/3}\).