Some addition to the generalized Riemann-Hilbert problem
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 3, p. 561-576

We consider the generalized Riemann-Hilbert problem for linear differential equations with irregular singularities. If one weakens the conditions by allowing one of the Poincaré ranks to be non-minimal, the problem is known to have a solution. In this article we give a bound for the possibly non-minimal Poincaré rank. We also give a bound for the number of apparent singularities of a scalar equation with prescribed generalized monodromy data.

Nous considérons le problème de Riemann-Hilbert généralisé pour des équations différentielles linéaires avec singularités irrégulières. Si on affaiblit les conditions en autorisant que l’un des rangs de Poincaré ne soit pas minimal, il est connu que le problème a une solution. Dans cet article nous donnons une borne pour le rang de Poincaré ainsi obtenu. Nous donnons aussi une borne pour le nombre de singularités apparentes de l’équation scalaire avec une donnée de monodromie généralisée prescrite.

@article{AFST_2009_6_18_3_561_0,
     author = {Gontsov, R.R. and Vyugin, I.V.},
     title = {Some addition to the generalized Riemann-Hilbert problem},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 18},
     number = {3},
     year = {2009},
     pages = {561-576},
     doi = {10.5802/afst.1214},
     mrnumber = {2582441},
     zbl = {1200.34110},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2009_6_18_3_561_0}
}
Gontsov, R.R.; Vyugin, I.V. Some addition to the generalized Riemann-Hilbert problem. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 3, pp. 561-576. doi : 10.5802/afst.1214. http://www.numdam.org/item/AFST_2009_6_18_3_561_0/

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