%0 Journal Article
%T On the reduction of the degree of linear differential operators
%A Marcin Bobie¨˝ski
%A Lubomir Gavrilov
%J Mathematics
%D 2010
%I arXiv
%R 10.1088/0951-7715/24/2/002
%X 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.
%U http://arxiv.org/abs/1003.0629v1