4 problems

Let $X=\mathbf H_\mathbb R^n$ be real hyperbolic $n$-space, let $\Gamma<\operatorname{Isom}(X)$ be a discrete group, and let $\delta(\Gamma)$ denote its critical exponent. Consider…

Let $\Gamma$ be a geometrically finite group, let $\sigma$ be a representation parameter, let $\lambda\in{\mathfrak a}_{\mathbb C}^*$, and let $\varphi$ be the auxiliary parameter…

Let $n\geq 1$ and let $\Gamma$ be a discrete and torsion-free subgroup of $\mathrm{PU}(n,1)$ acting on the complex hyperbolic space $\mathbb{H}^{n}_{\mathbb{C}}$. Define the critic…

Let $X$ be a geometrically finite hyperbolic surface, and let the resonance-counting function and critical exponent be as in the paper. The paper establishes a main theorem and a t…