  In 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.
