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.
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.
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@article{CRMATH_2002__335_2_171_0, author = {Neto, Orlando and Silva, Pedro C.}, 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}, url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02436-6/} }
TY - JOUR AU - Neto, Orlando AU - Silva, Pedro C. TI - Holonomic systems with solutions ramified along a cusp JO - Comptes Rendus. Mathématique PY - 2002 SP - 171 EP - 176 VL - 335 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02436-6/ DO - 10.1016/S1631-073X(02)02436-6 LA - en ID - CRMATH_2002__335_2_171_0 ER -
%0 Journal Article %A Neto, Orlando %A Silva, Pedro C. %T Holonomic systems with solutions ramified along a cusp %J Comptes Rendus. Mathématique %D 2002 %P 171-176 %V 335 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02436-6/ %R 10.1016/S1631-073X(02)02436-6 %G en %F CRMATH_2002__335_2_171_0
Neto, Orlando; Silva, Pedro C. 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. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02436-6/
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