5 problems

GinOE number variance scaling limits. As $N\to\infty$, the following limits are expected. For fixed $a\in(0,1)$,

Let $S(t)$ be the argument function of the Riemann zeta function, and let $\gamma_0$ be Euler's constant. For $\delta>0$, consider the mean square of the increment…

Smooth Gaussian-prime variance conjecture. The variance satisfies

Let $\mathcal E(n)$ be the projected lattice points on $S^2$, let $N_n$ be their number, and let $\sigma$ denote normalized spherical area. For a spherical cap or annulus…

Let $E_\beta^{(\cdot)}(n;J)$ denote the probability of exactly $n$ particles in $J$, let $n_J$ be the corresponding particle number, and let $\langle n_J\rangle$ and…