An estimate of the roots of b-functions by Newton polyhedra
type: Item
instance of: scholarly article
title: An estimate of the roots of b-functions by Newton polyhedra
zbMATH Open document ID: 0535.35002
author: Mitsuo Kato
published in: Proceedings of the Japan Academy. Series A
publication date: 1981-01-01T00:00:00Z
review text: By \textit{I. N. Bernshtejn} [Funkts. Anal. Prilozh. 6, Nr. 4, 26-40 (1972; Zbl 0282.46038)] and \textit{J.-E. Björk} [Rings of differential operators (1979; Zbl 0499.13009)], any \(f\in {\mathcal O}\), the set of germs of holomorphic functions at the origin of \(C^{n+1}\), there exist P(s)\(\in {\mathcal D}[s]\), \({\mathcal D} ={\mathcal O}[\partial /\partial x_ 0,...,\partial /\partial_ n]\) such that \(P(s)f^{s+1}=b(s)f^ s\). Making use of the theory of b-functions by \textit{T. Yano} [Publ. Res. Inst. Math. Sci. 14, 111-202 (1978; Zbl 0389.32005)], the author proves that any root of \(b(s)/(s+1)\geq 1/\inf \{t;\quad(t,t,...,t)\in \Gamma_+(f)\}\) when f has an isolated singularity and is nondegenerated.
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 32A10
zbMATH DE Number: 3849671
zbMATH Keywords: Newton polyhedra
zbMATH Keywords: germs of holomorphic functions
zbMATH Keywords: b-functions
zbMATH Keywords: isolated singularity
reviewed by: J. Kajiwara
MaRDI profile type: Publication
full work available at URL: pjaa.57.496
OpenAlex ID: W2077436598
cites work: The analytic continuation of generalized functions with respect to a parameter
cites work: Q3964695
cites work: Q4047653
cites work: Newton polyhedra and estimation of oscillating integrals
cites work: On the theory of b-functions
DOI: 10.3792/PJAA.57.496
description: scientific article; zbMATH DE number 3849671