Uniqueness theorems for holomorphic functions on compact Riemann surfaces (Q2778270)

In this note the author formulates theorems on shared values and ramified values for holomorphic mappings on compact Riemann surfaces. Two non-constant holomorphic maps \(p,q:X\to Y\) share the value \(y\in Y\) if \(p^{-1}(\{y\})=q^{-1}(\{y\})\). Among other results the author proves that the number of shared values for distinct meromorphic functions on a compact Riemann surface with positive genus \(g\) is bounded by \(2+2\sqrt{g}\).