Two-variable zeta functions and regularized products
Number Theory
2007-05-23 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.math/0210269,
title = {Two-variable zeta functions and regularized products},
author = {Christopher Deninger},
journal= {arXiv preprint arXiv:math/0210269},
year = {2007}
}