Comptes Rendus
no. 2
Holonomic systems with solutions ramified along a cusp
[Systèmes holonomes avec solutions ramifiées le long d'un cusp]
Orlando Neto1 ; Pedro C. Silva1
1 CMAF, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal
Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 171-176.

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 kFk−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 kFk−1 hypergeometric functions on the Riemann sphere.

Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02436-6
Orlando Neto 1 ; Pedro C. Silva 1

1 CMAF, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal 
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     title = {Holonomic systems with solutions ramified along a~cusp},
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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/

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[2] J.-E. Bjork Analytic 𝒟-modules and Applications, Kluwer Academic, 1993

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

[4] A.H. Levelt Hypergeometric functions, Indag. Math., Volume 23 (1961), pp. 361-403

[5] O. Neto A microlocal Riemann–Hilbert correspondence, Comp. Math., Volume 127 (2001), pp. 229-241

[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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