2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65334In this paper we prove a regularized product expansion for the two-variable zeta functions of number fields introduced by van der Geer and Schoof. The proof is based on a general criterion for zeta-regularizability due to Illies. For number fields of non-zero unit rank our method involves a result of independent interest about the asymptotic behaviour of certain oscillatory integrals in the geometry of numbers. We also explain the cohomological motivation for the paper.Number TheoryAlgebraic Geometry11M38; 11M41; 11H41; 14G40text