4 problems

Let $q$ be a prime power, let $\Theta(t)\in\mathbb{F}_q(\!(t^{-1})\!)$ be quadratic irrational, and let $P(t)\in\mathbb{F}_q[t]$ be irreducible. For $n,k\in\mathbb{N}$, define … Fu…

Let $P(t)\in\mathbb{F}_q[t]$ be irreducible. For a lattice $\Lambda_0\in\mathcal{L}_2$, let $\mathbb{T}_P(\Lambda_0)$ be its $P(t)$-Hecke tree, and let…

Rational-ray escape-of-mass conjecture. For any rational $\xi\in\Omega$, the measures $\mu_{x_n^\xi}$ converge to the zero measure.

Generic equidistribution conjecture. For almost every $\xi\in\Omega$, the averages