Abstract

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^g(s) for R(s) ≫ 0, whose definition involves closed geodesics and their Poincaré maps. We show that Z^g extends meromorphically to the entire plane and that its leading coeficient at s = 0 equals the quotient of the equivariant torsion over the equivariant L²-torsion.

Authors