2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70812Let (R,m,k) be an excellent, local, normal ring of characteristic p with a perfect residue field and dim R=d. Let M be a finitely generated R-module. We show that there exists a real number beta(M) such that lambda(M/I^[q]M) = e_{HK}(M) q^d + beta(M) q^{d-1} + O(q^{d-2}).11 pages, minor changes, additional referencesCommutative Algebra13D40text