Orders of Zeros of Polynomials on Trajectories of Solutions of a System of Linear Differential Equations with Regular Singular Points

摘要

We consider a system of the form dy/dz = B(z)y (1) consisting of p linear meromorphic differential equations defined on the Riemann sphere and having regular singularities at points a1 , . . . , an (i.e., the system has singularities such that in sectorial neighborhoods of these points any solution of the system is a function of at most power-law growth).