3 problems

Let $\zeta(s)$ be the Riemann zeta function, let $\vartheta(t)$ be the Riemann–Siegel theta function, and let $S(t)=\arg\zeta(\frac{1}{2}+it)$. Let $f_0(t)$ denote the function use…

Crowley's argument formula conjecture. For every $n\geqslant1$, the argument at the zero satisfies

Let $\zeta(s)$ be the Riemann zeta-function, and let the critical line be $s=\frac{1}{2}+it$ with $t\in\mathbb{R}$. Density conjecture. The set of values … is dense in the complex…