The second moment of $S_n(t)$ on the Riemann hypothesis

Andrés Chirre, Emily Quesada-Herrera

Let $S(t)=\frac{1}{\pi }\arg \zeta (1/2+it)$ be the argument of the Riemann zeta-function at the point $\frac{1}{2}+it$. For $n\ge 1$ and $t>0$ define its antiderivatives a…