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Two-variable zeta functions and regularized products

Christopher Deninger
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Abstract

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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Christopher Deninger. 2002-10-17. Two-variable zeta functions and regularized products. https://arxiv.org/abs/math/0210269

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