10 problems

Meromorphic-power conjecture. Then there is an integer $N$ such that

Selberg-zeta divisor conjecture. (i) The cohomology groups $H^*(\Gamma,C^{-\omega}(\Lambda,V^k(\sigma_\lambda,\varphi)))$ and…

Selberg-zeta cohomology conjecture. The order of the singularity of $Z_{S,\sigma}$ at $\lambda$ is related to the dimensions of the cohomology groups

Patterson's finiteness conjecture. The dimensions of the spaces

Optimal-exponent conjecture. The optimal exponent in this error estimate is $\frac{1}{2}+\varepsilon$, owing to an analogue of the Riemann hypothesis for the Selberg zeta function…

Let $\Gamma$ be the cofinite Fuchsian group defining the hyperbolic surface $\Gamma \backslash \mathbb{H}$, and let $\Psi_{\Gamma}(x)$ be its Chebyshev-like counting function. Writ…

Jakobson–Naud's conjecture. There are only finitely many zeros in the half-plane

Let $\Gamma$ be an arithmetic group, let $\zeta_{\Gamma}(s)$ be the associated Selberg zeta function, and let $\varepsilon_{\Gamma}(s)\in\{\pm1\}$ be the sign factor appearing in t…

Let $\Gamma_{\mathcal C_0,\eta}$ be the quasi-Fuchsian group associated with the marked Riemann surfaces $\mathcal C_0$ and $\mathcal C=\mathcal C_0^\eta$. Let…

Let $M$ be a finite-volume Riemann surface, let $Z_M$ denote its Selberg zeta function, and let the discrete eigenvalues of the Laplacian on $M$ have associated eigenspaces. Bounde…