Functions of Bounded Characteristic

Abstract

A major part of the classical value distribution theory is based on the Poisson-Jensen formula. For the general theory of meromorphic functions f on Riemann surfaces R this is not a preferred method as even the first main theorem appears with a remainder that causes unnecessary complications. However, the approach has the advantage that log |f| on a regular subregion Ω can be decomposed. In the limit Ω → R valuable information is thus obtained provided f has bounded characteristic. It is this class M B of meromorphic functions of bounded characteristic that will occupy us in the present chapter.