Large Oscillations of the Argument of the Riemann Zeta-function

Andrés Chirre, Kamalakshya Mahatab

Let $S(t)$ denote the argument of the Riemann zeta-function, defined as $$S(t)=\frac{1}{\pi }\Im \log \zeta (1/2+it).$$ Assuming the Riemann hypothesis, we prove that $$ S(t)=Ω_{\pm}\bigg…