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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 238, Pages 86–96 (Mi tm346)  

This article is cited in 3 scientific papers (total in 3 papers)

Équations fonctionnelles associées à des fonctions analytiques

J. Briançon, Ph. Maisonobe, M. Merlea

a Université de Nice Sophia Antipolis
Full-text PDF (222 kB) Citations (3)
References:
Abstract: Let XX be a  XX, and denote by F=f1fpF=f1fp their product. Given a regular holonomic DXDX-module MM and a section mMmM, denote by B(x,f1,,fp,m)B(x,f1,,fp,m) the Bernstein–Sato ideal of C[s1,,sp]C[s1,,sp] consisting of polynomials b(s1,,sp)b(s1,,sp) such that there exists, in a neighborhood of xF1(0)xF1(0), a differential operator P(s1,,sp)DXCC[s1,,sp]P(s1,,sp)DXCC[s1,,sp] satisfying P(s1,,sp)mfs1+11fsp+1p=b(s1,,sp)mfs11fsppP(s1,,sp)mfs1+11fsp+1p=b(s1,,sp)mfs11fspp. Claude Sabbah proved that this ideal is nonzero. One can associate to the characteristic variety of the DX[s1,,sp]-module DX[s1,,sp]mfs11fspp a finite set Hf,m of hyperplanes in Cp. We prove that there exists a Bernstein–Sato polynomial (i.e., a nonzero member of the Bernstein–Sato ideal) which is a product of one variable polynomials if and only if the set Hf,m is contained in the union of the coordinate hyperplanes. In the two variables case (p=2) we prove that there exist a Bernstein–Sato polynomial the higher degree form of which vanishes on and only on the set Hf,m.
Received in November 2000
Bibliographic databases:
UDC: 512.7+517.5
Language: French
Citation: J. Briançon, Ph. Maisonobe, M. Merle, “Équations fonctionnelles associées à des fonctions analytiques”, Monodromy in problems of algebraic geometry and differential equations, Collected papers, Trudy Mat. Inst. Steklova, 238, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 86–96; Proc. Steklov Inst. Math., 238 (2002), 77–87
Citation in format AMSBIB
\Bibitem{BriMaiMer02}
\by J.~Brian{\c c}on, Ph.~Maisonobe, M.~Merle
\paper \'Equations fonctionnelles associ\'ees \`a des fonctions analytiques
\inbook Monodromy in problems of algebraic geometry and differential equations
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2002
\vol 238
\pages 86--96
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm346}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1969306}
\zmath{https://zbmath.org/?q=an:1026.32017}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 238
\pages 77--87
Linking options:
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  • https://www.mathnet.ru/eng/tm/v238/p86
  • This publication is cited in the following 3 articles:
    1. Wu L., “Characteristic Cycles Associated to Holonomic D-Modules”, Math. Z., 301:2 (2022), 2059–2098  crossref  mathscinet  isi  scopus
    2. Budur N., van der Veer R., Wu L., Zhou P., “Zero Loci of Bernstein-Sato Ideals-II”, Sel. Math.-New Ser., 27:3 (2021), 32  crossref  mathscinet  isi
    3. Bahloul R., “Construction of a remarkable element of the Bernstein–Sato ideal associated with two analytical plane curves”, Kyushu Journal of Mathematics, 59:2 (2005), 421–441  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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    Full-text PDF :160
    References:60
     
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