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Zbl 0578.12016
Bertrand, Daniel; Beukers, Frits
Équations différentielles linéaires et majorations de multiplicités. (Linear differential equations and upper bounds for multiplicities). (French)
[J] Ann. Sci. Éc. Norm. Supér. (4) 18, 181-192 (1985). ISSN 0012-9593

From the authors' abstract: "We establish an upper bound for the order, at one or several points, of certain functions associated to the solutions of a linear differential system on ${\bbfP}\sp 1({\bbfC})$. This sharpens previous results of Nesterenko, Chudnovsky and Osgood on Shidlovsky's lemma. To this aim, we extend to the case of irregular singularities a well-known global relation connecting the different exponents of a Fuchsian differential equation".
[F.Baldassarri]

MSC 2000:: *12H20 Abstract differential equations
34G10 Linear ODE in abstract spaces

Keywords: linear differential system; Shidlovsky's lemma; irregular singularities; exponents; Fuchsian differential equation

Cited in: Zbl 0717.11026 Zbl 0603.10034 Zbl 0589.12019

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