  We extend results of Bhagwat and Rajan on a strong multiplicity one property
for length spectrum to hyperbolic manifolds with cusps, showing that for two
even dimensional hyperbolic manifolds of finite volume, if all but finitely
many closed geodesics have the same length, then all closed geodesics have the
same length. When the set of exceptional lengths is infinite, but sufficiently
sparse, we can show that the two manifolds must have the same volume, and in
low dimensions also the same number of cusps. A main ingredient in our proof is
a generalization of a result of Selberg on the distribution of poles of
Eisenstein series to hyperbolic manifolds.
