Deninger, Christopher

Two-variable zeta functions and regularized products

Doc. Math. (Bielefeld) Extra Vol. Kazuya Kato's Fiftieth Birthday, 227-259 (2003)


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.

Mathematics Subject Classification

11M36, 11M41


zeta function, zeta regularization, oscillatory integral, metrized lattice