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Équations différentielles linéaires et majorations de multiplicités. (Linear differential equations and upper bounds for multiplicities). (French) Zbl 0578.12016

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 \({\mathbb{P}}^ 1({\mathbb{C}})\). 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”.
Reviewer: F.Baldassarri

MSC:

12H20 Abstract differential equations
34G10 Linear differential equations in abstract spaces
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References:

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