Title: Poles of Archimedean zeta functions for analytic mappings
Authors: Leon-Cardenal, E ×
Veys, Willem
Zuniga-Galindo, W. A #
Issue Date: Jan-2013
Publisher: London Mathematical Society
Series Title: Journal of the London Mathematical Society vol:87 pages:1-21
Abstract: Let f=(f1, …, fl):U→Kl, with K=ℝ or ℂ, be a K-analytic mapping defined on an open set U⊂Kn, and let Φ be a smooth function on U with compact support. In this paper, we give a description of the possible poles of the local zeta function attached to (f, Φ) in terms of a log-principalization of the ideal ℐf=(f1, …, fl). When f is a non-degenerate mapping, we give an explicit list for the possible poles of ZΦ(s, f) in terms of the normal vectors to the supporting hyperplanes of a Newton polyhedron attached to f, and some additional vectors (or rays) that appear in the construction of a simplicial conical subdivision of the first orthant. These results extend the corresponding results of Varchenko to the case l≥1, and K=ℝ or ℂ. In the case l=1 and K=ℝ, Denef and Sargos proved that the candidate poles induced by the extra rays required in the construction of a simplicial conical subdivision can be discarded from the list of candidate poles. We extend the Denef–Sargos result to arbitrary l≥1. This yields, in general, a much shorter list of candidate poles, which can, moreover
ISSN: 0024-6107
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

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