## B-functions and holonomic systems. Rationality of roots of B-functions.(English)Zbl 0354.35082

### MSC:

 35S99 Pseudodifferential operators and other generalizations of partial differential operators
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### References:

 [1] Bernstein, I. N.: The analytic continuation of generalized functions with respect to a parameter. Functional Anal. Appl.6, 26-40 (1972) [2] Bernstein, I. N., Gelfand, S. I.: Meromorphy of the functionP ?. Functional Anal. Appl.3, 84-86 (1969) [3] Björk, J. E.: Dimensions over Algebras of Differential Operators. Preprint · Zbl 0313.16027 [4] Kashiwara, M.: Algebraic study of systems of partial differential equations. Master’s thesis, Univ. of Tokyo, 1971 (Japanese) · Zbl 0877.35003 [5] Kashiwara, M.: On the maximally overdetermined system of linear differential equations. I. Publ. RIMS, Kyoto Univ.10, 563-579 (1975) · Zbl 0313.58019 [6] Kashiwara, M., Kawai, T.: Micro-local properties of $$\Pi _{j = 1}^n f_{j + e}^{s_j }$$ . Proc. Japan Acad.51, 270-272 (1975) · Zbl 0304.35068 [7] Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero, I. II. Ann. of Math.79, 109-326 (1964) · Zbl 0122.38603 [8] Malgrange, B.: Le polynome de Bernstein d’une singularité isolée. Lecture notes in Math.459, pp. 98-119, Berlin-Heidelberg-New York: Springer [9] Malgrange, B.: Sur les polynomes de I. N. Bernstein, Uspekhi Mat. Nauk29 (4), 81-88 (1974) [10] Sato, M.: Theory of prehomogeneous vector spaces. Sugaku no Ayumi 15-1 (1970) (noted by T. Shintani) [11] Sato, M., Kawai, T., Kashiwara, M.: Microfunctions and Pseudo-differential Equations, Proc. Katata Conf. Lecture Notes in Math.287, pp. 263-529. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0277.46039 [12] Sato, M., Shintani, T.: On zeta functions associated with prehomogeneous vector space. Annals of Math.100, 131-170 (1974) · Zbl 0309.10014 [13] Proceeding of Symposium ?Singularity of hypersurfaces andb-functions?, Surikaisekikenkyushokokyuroku 225 (1975) [14] Yano, T.: The theory ofb-functions. Mater’s thèse presented to Kyoto University (1975) (here we find many interesting examples ofb-functions)
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