Singularities of solutions of the Fuchsian Cauchy problem with ramified data

Abstract

We concretely construct the solution of the singular Cauchy problem for a Fuchsian partial differential operator of weight one by means of hypergeometric representations and study what kind of singularities appear on the characteristic surfaces determined by the principal part of the operator. In particular we investigate how the singularities are characterized not only by the principal part but also by the subprincipal part restricted at the origin and the ramification index of Cauchy data.