×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI EuDML
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 · doi:10.2977/prims/1195192011
[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 · doi:10.3792/pja/1195518633
[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 · doi:10.2307/1970486
[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 · doi:10.2307/1970844
[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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.