9 problems

Assume the Riemann Hypothesis and consider the local point process of the nontrivial zeros of the zeta function, rescaled by the mean spacing. The gap between two consecutive point…

Gap conjecture. It is conjectured that

Unbounded normalized-gap conjecture. The parameter satisfies $\lambda'=\infty$. This conjecture is motivated by analogies with random matrix theory. The paper argues instead that…

Farmer–Ki conjecture. If $m'(v)\gg v^\alpha$ for some $\alpha<2$, then $m(v)>0$ for all $v>0$.

Let $k$ be a parameter, and let $a(k)$ and $g(k)$ denote the arithmetic and random-matrix factors in the conjectural moment formula. Hughes's derivative moment conjecture. One has…

Assume the Riemann Hypothesis, and let $m(\varepsilon)$ and $m'(\varepsilon)$ be the normalized zero-gap distribution functions defined by … … where $w$ is the indicator function o…

Assume the Riemann Hypothesis. Let $w(x)$ be the indicator function of the unit interval, and define … … where $\gamma$ and $\gamma'$ are ordinates of zeros of $\zeta(s)$ and…

Assume the Riemann Hypothesis. Let $w(x)$ be the indicator function of the unit interval, and define … … where $\gamma$ and $\gamma'$ are ordinates of zeros of $\zeta(s)$ and…

Unbounded normalized-gap conjecture. The normalized gaps between consecutive zeros are arbitrarily large; equivalently,