In this paper we express the equivariant torsion of an Hermitian locally symmetric space in terms of geometrical data from closed geodesics and their Poincaré maps. For a Hermitian locally symmetric space Y and a holomorphic isometry g we define a zeta function Z(s) for <(s) 0, whose definition involves closed geodesics and their Poincaré maps. We show that Z extends meromorphically to the enti...

– This note corrects and complements our paper entitled “Scattering matrices and scattering geodesics of locally symmetric spaces” (Ann. Sci. Éc. Norm. Sup. 34 (2001) 441–469).  2002 Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ. – Nous apportons des corrections et des compléments à notre article intitulé “Scattering matrices and scattering geodesics of locally symmetric spaces” paru...

We introduce hyperbolic and asymptotic compactiications of metric spaces and apply them to locally symmetric spaces ?nX. We show that the reductive Borel{Serre compactiication ?nX RBS is hyperbolic and, as a corollary, get a result of Borel, and Kobayashi{Ochiai that the Baily{Borel compactiication ?nX BB is hyperbolic. We prove that the hyperbolic reduction of the toroidal compactiications ?nX...

Let X = G/K be a Riemannian symmetric space of the noncompact type, Γ ⊂ G a discrete, torsion-free, cocompact subgroup, and let Y = Γ\X be the corresponding locally symmetric space. In this paper we explain how the Harish-Chandra Plancherel Theorem for L(G) and results on (g,K)-cohomology can be used in order to compute the L-Betti numbers, the Novikov-Shubin invariants, and the L-torsion of Y ...

We explain how the Transference Principles from Diophantine approximation can be interpreted in terms of geometry of the locally symmetric spaces Tn = SO(n)\SL(n,R)/SL(n,Z) with n ≥ 2, and how, via this dictionary, they become transparent geometric remarks and can be easily proved. Indeed, a finite family of linear forms is naturally identified to a locally geodesic ray in a space Tn and the wa...

Contents 1 Holomorphic torsion 5 2 The trace of the heat kernel 8 2.

In this paper, we address the equivalence of the analytic and probabilistic notions of harmonicity in the context of general symmetric Hunt processes on locally compact separable metric spaces. Extensions to general symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper. AMS 2000 Mathematics Subject Classification: Primary 60J45, 3...

We give a geometric interpretation of the maximal Satake compactification of symmetric spaces X “ G{K of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable G-invariant Finsler metric on X. As an application, we establish the existence of natural bordifications, as orbifolds-with-corners, of locally symmetric spaces X{Γ for arbitrary discrete subgroups ...