Holonomic systems with solutions ramified along a cusp

Orlando Neto; Pedro C. Silva

doi:10.1016/S1631-073X(02)02436-6

Holonomic systems with solutions ramified along a cusp
[Systèmes holonomes avec solutions ramifiées le long d'un cusp]

Orlando Neto ¹ ; Pedro C. Silva ¹

¹ CMAF, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 171-176.

Résumé
Abstract

On classifie les systèmes holonomes d'équations (micro) differentielles de multiplicité un dont le support est un espace analytique complexe Lagrangien, singulier, irréductible et contenu dans une sous-varieté lisse de codimension maximal. On montre que leur solutions sont en rapport avec des fonctions _kF_k−1 hypergeométriques sur la sphère de Riemann.

We classify the holonomic systems of (micro) differential equations of multiplicity one along a singular Lagrangian irreducible variety contained in an involutive submanifold of maximal codimension. We show that their solutions are related to _kF_k−1 hypergeometric functions on the Riemann sphere.

Accepté le : 2002-05-06
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02436-6

Affiliations des auteurs :

Orlando Neto ¹ ; Pedro C. Silva ¹

¹ CMAF, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

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     author = {Orlando Neto and Pedro C. Silva},
     title = {Holonomic systems with solutions ramified along a~cusp},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {171--176},
     publisher = {Elsevier},
     volume = {335},
     number = {2},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02436-6},
     language = {en},
}

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Orlando Neto; Pedro C. Silva. Holonomic systems with solutions ramified along a cusp. Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 171-176. doi : 10.1016/S1631-073X(02)02436-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02436-6/

Bibliographie
Cité par

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[3] M. Kashiwara; T. Kawai On holonomic systems of microdifferential equations III, Publ. Res. Inst. Math. Sci., Volume 17 (1981), pp. 813-979

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[6] P. Schapira Microdifferential Systems in the Complex Domain, Springer-Verlag, 1985

[7] M. Sato; M. Kashiwara; T. Kimura; T. Oshima Micro-local analysis of prehomogeneous vector spaces, Invent. Math., Volume 62 (1980), pp. 117-178

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