EQUIVARIANT TORSION OF LOCALLY SYMMETRICAL SPACES

In this paper we express the equivariant torsion of an Hermitian local ly symmetric space in terms of geometrical data from closed geodesics and their Poincare maps. For a Hermitian locally symmetric space Y and a holomorphic isometry theta we define a zeta function Z(theta)(s) fo r R(s) >> 0, whose definition involves closed geodesics and their Poin care maps. We show that Z(theta) extends meromorphically to the entire plane and that its leading coefficient at s = 0 equals the quotient o f the equivariant torsion over the equivariant L-2-torsion.