B-functions and holonomic systems

@article{Kashiwara1976BfunctionsAH,
  title={B-functions and holonomic systems},
  author={Masaki Kashiwara},
  journal={Inventiones mathematicae},
  year={1976},
  volume={38},
  pages={33-53}
}
  • M. Kashiwara
  • Published 1 February 1976
  • Mathematics
  • Inventiones mathematicae
A b-function of an analytic function f(x) is, by definition, a gcnerator of the ideal formed by the polynomials b(s) satisfying P(s, x, Dx) f (x)" + 1 = b(s) f(x) ~ for some differential operator P(s, x, Dx) which is a polynomial on s. Professor M.Sato introduced the notions of "a-function", "b-function" and "'c-function" for relative invariants on prehomogeneous vector spaces, when he studied the fourier transforms and ~-functions associated with them (see [10, 12]). He defined, in the same… 
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References

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The purpose of this paper is to present finiteness theorems and several properties of cohomologies of holomorphic solution sheaves of maximally overdetermined systems of linear differential
On zeta functions associated with prehomogeneous vector spaces.
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TLDR
In this note, certain families of Dirichlet series are constructed that satisfy functional equations and an arithmetical application of the results are indicated.
Sur les polynômes de I. N. Bernstein
© Séminaire Équations aux dérivées partielles (Polytechnique) (École Polytechnique), 1973-1974, tous droits réservés. L’accès aux archives du séminaire Équations aux dérivées partielles
Le polynome de Bernstein d'une singularit6 isolee. Lecture notes in Math
  • Le polynome de Bernstein d'une singularit6 isolee. Lecture notes in Math
The theory of b functions. Mater's these presented to Kyoto University (1975) (here we find many interesting examples of b-functions)
  • The theory of b functions. Mater's these presented to Kyoto University (1975) (here we find many interesting examples of b-functions)
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