Recently, Solomon has introduced a zeta function which counts sublattices of a given lattice over an order ([5]). Let us recall the definition of this zeta function. Let I be a (finitedimensional) semisimple algebra over the rational fieldQ or over the j!?-adicfieldQp, and let A be an order in I. A is a Z-order when I is a Q-algebra, while A is a Zp-order when 2 is a Qp-algebra, where Zp is the ring of p-adic integers. Throughout this paper, p stands for a rational prime and the subscript p indicates the p-dAic completion. Let V be a finitelygenerated left I'-module, and let L be a full//-lattice in V. Solomon's zeta function is defined as