2 problems

Kurlberg–Rudnick's conjecture. As $N\to\infty$ through primes, the limiting distribution of the normalized matrix elements $F_j^{(N)}$ is the distribution of

Quadratic-form IID conjecture. For every $\nu\in\mathbb{Z}$, $Y_\nu(\psi)$ has limiting distribution equal to that of $\operatorname{tr}(U_\nu)$, where $U_\nu$ is Haar-random in…