Newton polyhedra and Igusa's local zeta function
type: Item
instance of: scholarly article
title: Newton polyhedra and Igusa's local zeta function
zbMATH Open document ID: 0994.11038
author: Jan Denef
author: Kathleen Hoornaert
published in: Journal of Number Theory
publication date: 2002-06-04T00:00:00Z
review text: The authors consider Igusa's local zeta function \(Z_f(s) = \int_{{\mathbb Z}_p} |f(x)|^s |d x|\) associated with a polynomial \(f(x_1,\dots,x_n)\in{\mathbb Z}_p[x_1,\dots,x_n]\). For \(f(0)=0\) and \(f\) non-degenerate over the finite field \({\mathbb F}_p\) with respect to all the faces of its Newton polyhedron \(\Gamma(f)\), they obtain an explicit formula for \(Z_f(s)\). Among applications we mention the study of the largest real pole different from \(-1\) of Igusa's local zeta function. The paper also contains examples and explicit computations.
reviewed by: Doru Ştefănescu
Mathematics Subject Classification ID: 11S40
Mathematics Subject Classification ID: 14G10
zbMATH DE Number: 1749022
zbMATH Keywords: Newton polyhedra
zbMATH Keywords: local zeta functions
MaRDI profile type: Publication
OpenAlex ID: W2066751699
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DOI: 10.1006/JNTH.2000.2606
description: scientific article; zbMATH DE number 1749022