Two-variable zeta functions and regularized products

Details Two-variable zeta functions and regularized products Two-variable zeta functions and regularized products

2002-10-17

arxiv.org/abs/math/0210269v1

Mathematics

Number Theory

Scientific paper

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.

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