4 problems

Let $f$ be a hyperbolic rational map, let $Z(s)$ denote its dynamical zeta function, let \\{\mu_j\} be the zeros of $Z$ counted with multiplicity, and let $\delta$ be the dimensi…

Essential spectral gap conjecture. For every $\omega\in\mathcal{H}^1(X)$,

Let $(\Sigma,g)$ be a negatively curved oriented compact Riemannian manifold of dimension $n>2$, and let $\alpha$ be an acyclic unitary representation of $\pi_1(\Sigma)$. Let…

Holomorphic extension and zero localization conjecture. The semiclassical zeta function $Z_{sc}(s)$ for contact Anosov flows has a holomorphic extension to the whole complex plane…