Zeta functions of virtually nilpotent groups

We prove that the subgroup and the normal zeta functions of finitely generated virtually nilpotent groups can be written as a finite sum of Euler products of cone integrals and we deduce from this that they have rational abscissae of convergence and meromorphic continuation. We also define Mal'cev completions of a finitely generated virtually nilpotent group and we prove that the subgroup growth and the normal subgroup growth of the latter is an invariant of its $\mathbb{Q}$-Mal'cev completion.