4 problems

Square-root error conjecture. For every $\epsilon>0$,

Let $g\in \operatorname{SL}_{2}(\mathbb{R})$. For parameters $\ell$, $\delta$, $L$, and $\heartsuit$, consider pairs $\gamma_1,\gamma_2\in R(\ell;g)$ lying in…

Homogeneous-space counting conjecture. There exists an exhausting compact family $\mathcal{B}^Z=(B_R^Z)_{R>0}$ of $Z$ such that the quadruple…

Let $(a,b)$ be a strongly regular semisimple collection of invariants with $a_i,b_i\in\mathcal{O}_E^{\sigma=(-1)^i}$, allowing arbitrary $b_0\in\mathcal{O}_F$. Let $\Delta_{a,b}$ b…