Let G be a connected, semisimple Lie group with finite center and without compact factors, F a discrete uniform subgroup of G, U the unitary representation of G on L2(F\G) and [U] the equivalence class of U. For each class co in the unitary dual E(G) of G, let nr(co) be the multiplicity of co in [U]. It is well known [6] that [U] =~nr(m)c0, a discrete direct sum, where nr(co) 0 only for a countable number of o. The function n r may be called the spectral function of F. In [5], Gangolli asked the question to what extent does n r determine F? If F, F' are two discrete uniform subgroups of G, then does n r = n r, imply that F is isomorphic to F'?