4 problems

Gath's conjecture. The optimal order of the error term is $2q-1$; that is, the infimum of the exponents $\kappa$ for which $|\mathcal E_q(t)|\lesssim t^\kappa$ holds equals $2q-1$.…

Let $\Lambda_N^{\mathrm{sph}}$ denote the spherical truncation and let $S^{\mathrm{sph}}(N)$ be its associated incidence quantity. Spherical truncation incidence-growth conjecture.…

Let $G=\operatorname{SO}(n,1)^\circ$, let $\rho=\tfrac{n-1}{2}$, and let $\Gamma<G(\mathbb{Z})$ be geometrically finite and Zariski dense, with critical exponent $\delta$. Fix…

Let $G=\operatorname{SO}(n,1)^\circ$, let $\rho=\tfrac{n-1}{2}$, and let $\Gamma<G(\mathbb{Z})$ satisfy $[G(\mathbb{Z}):\Gamma]<\infty$. Fix $o\in\mathbb H^n$, let $d$ be hyperboli…