The First Main Theorem in the Theory of Meromorphic Functions

Abstract

In the present and in the following chapters we shall concern ourselves with the theory of those analytic functions that are of rational character, or as one expresses this more briefly, meromorphic at every point of a given schlicht region G. Such a function w = w(z) is hence regular in G except for poles; if the latter are infinite in number, they accumulate toward the boundary Γ of G. We shall further restrict ourselves to the simplest case, where G is simply connected; by the mono-dromy theorem, w(z) is then single-valued in G.