Equivariant torsion of locally symmetric spaces

Anton Deitmar

Vol. 182 (1998), No. 2, 205–227

DOI: 10.2140/pjm.1998.182.205

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 coefficient at s = 0 equals the quotient of the equivariant torsion over the equivariant L²-torsion.

Milestones

Received: 31 October 1995

Published: 1 February 1998