4 problems

Let $\Gamma=SL_2(\mathbb{Z})$, let $\Omega\subset\Gamma\backslash\mathbb{H}$ be a fixed compact regular set, and let $\mu$ denote hyperbolic measure. Write $\xi(s)$ for the complet…

Let $X=\Gamma\backslash\mathbb{H}$ have volume $\operatorname{vol}(X)$, let $\Omega\subset X$ be any compact and sufficiently regular subset, and define … If … then…

Let $\Gamma=\operatorname{SL}_2(\mathbb{Z})$, let $\mathbb{H}$ be the upper half-plane, and let $g\in\mathcal{B}_0(\Gamma)$ be a Hecke–Maaß eigenform normalised by…

Gaussian moments conjecture. For every nonnegative integer $n$,