  A general approach to proving that the length spectrum of a compact
Riemannian manifold is an invariant of the Laplace spectrum comes from
considering the wave trace, a spectrally determined tempered distribution. The
Poisson relation states that the singularities of the wave trace can only occur
at lengths of closed geodesics. Proving that the Poisson relation is an
equality; i.e., every length of a closed geodesic is a singularity of the wave
trace, yields an effective means of recovering the length spectrum from the
Laplace spectrum. Regarding spaces of constant curvature this is known to be
true for spaces of constant negative curvature. Continuing the study of space
forms, we show that the Poisson relation is an equality for all flat manifolds,
homogeneous lens spaces and three-dimensional lens spaces with fundamental
group of prime order.
