5 problems

Let $S$ denote the multiset of ordinates of the nontrivial zeros of the Riemann zeta function. For $a>0$, define the continuous function $H_a:\mathbb{R}_{>0}\to\mathbb{C}$ by … whe…

Limiting-distribution conjecture. For every $a>0$ there is a Borel function $f_a:\mathbb{C}\to\mathbb{R}$ satisfying

GUE hypothesis. For $n\geq 1$ and any $\varphi\in\mathcal{S}(\mathbb{R}^n)$,

Let $G(s)$ be the function considered above, and let $T$ tend to infinity. Mean-square conjecture. … The preceding theorem gives the unconditional bounds…

Derivative-zero density conjecture. If $m'(\nu)\gg\nu^\alpha$ for some $\alpha<2$, then $m(\nu)>0$ for all $\nu>0$. This is proposed as a refinement of Soundararajan's conjecture.…