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

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.

Abstract
Résumé

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.

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.

Accepted: 2002-05-06
Published online: 2002-01-01

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

Author's affiliations:

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},
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     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/

References
Cited by

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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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