On the distribution of values of the argument of the Riemann zeta-function

Aleksandar Ivić, Maxim Korolev

Let $S(t):=\frac{1}{\pi }\arg \zeta (\frac{1}{2}+it)$. We prove that, for $T^{27/82+\epsilon }\le H\le T$, we have $$ {\rm mes}\Bigl\{t\in [T, T+H…