Geodesic
Two-variable zeta functions and regularized products
Documenta mathematica, Kazuya Kato's Fiftieth Birthday (2003), pp. 227-259.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 11M36, 11M41
Keywords: zeta function, zeta regularization, oscillatory integral, metrized lattice 
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Deninger, Christopher. Two-variable zeta functions and regularized products. Documenta mathematica, Kazuya Kato's Fiftieth Birthday (2003), pp. 227-259. http://geodesic.mathdoc.fr/item/DOCMA_2003__S6__a16/