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arXiv · 1003.0629

On the reduction of the degree of linear differential operators

Marcin Bobieński·Lubomir Gavrilov
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Abstract

Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type.

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Marcin Bobieński, Lubomir Gavrilov. 2010-03-02. On the reduction of the degree of linear differential operators. https://doi.org/10.1088/0951-7715%2F24%2F2%2F002

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