Geodesic
Refined Fuchs inequalities for systems of linear differential equations
Izvestiya. Mathematics , Tome 68 (2004) no. 2, pp. 259-272

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We refine the Fuchs inequalities obtained by Corel for systems of linear meromorphic differential equations given on the Riemann sphere. Fuchs inequalities enable one to estimate the sum of exponents of the system over all its singular points. We refine these well-known inequalities by considering the Jordan structure of the leading coefficient of the Laurent series for the matrix of the right-hand side of the system in the neighbourhood of a singular point. 
@article{IM2_2004_68_2_a2,
     author = {R. R. Gontsov},
     title = {Refined {Fuchs} inequalities for systems of linear differential equations},
     journal = {Izvestiya. Mathematics },
     pages = {259--272},
     publisher = {mathdoc},
     volume = {68},
     number = {2},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2004_68_2_a2/}
}
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R. R. Gontsov. Refined Fuchs inequalities for systems of linear differential equations. Izvestiya. Mathematics , Tome 68 (2004) no. 2, pp. 259-272. http://geodesic.mathdoc.fr/item/IM2_2004_68_2_a2/