Logarithmic singularities of Fuchs equations, and a criterion for the monodromy group to be finite
Consider the linear differential equation (*) \(y^{(n)}+a_ 1(x)y^{(n-1)}+...+a_ n(x)y=0\), where the coefficients \(a_ 1,...,a_ n\) are complex rational functions. The author considers two basic questions regarding (*). First, under what conditions are logarithmic terms absent from the asymptotic expansion of a solution in the neighborhood of a singular point? And second, when is the monodromy group of (*) finite? Both questions are reformulated in terms of appropriate properties of the Hall group associated with (*).
scientific article; zbMATH DE number 3875711