Abstract We show that the Ruelle dynamical zeta function on a closed odd dimensional locally symmetric space twisted by an arbitrary flat vector bundle has meromorphic extension to whole complex plane and its leading term in Laurent series at zero point is related regularised determinant of Laplacian Cappell–Miller. When close acyclic unitary one, we regular value equal valued analytic torsion ...

We give quantitive estimates for the number of locally symmetric spaces of a given type with bounded volume. Explicitly, let S be a symmetric space of non-compact type without Euclidean de Rham factors. Then, after rescaling appropriately the Riemannian metric, the following hold. Theorem A If rank(S) = 1 and S ≇ H2,H3, then there are at most V V Riemannian manifolds, locally isometric to S, wi...

We establish the equivalence of the analytic and probabilistic notions of subharmonicity in the framework of general symmetric Hunt processes on locally compact separable metric spaces, extending an earlier work of the first named author on the equivalence of the analytic and probabilistic notions of harmonicity. As a corollary, we prove a strong maximum principle for locally bounded finely con...