Nevanlinna Theory of Algebroid Functions on Complete Kähler Manifolds

In this paper, we generalize the classical Nevanlinna theory of algebroid functions from $\mathbb{C}$ to a complete Kähler manifold with either non-negative Ricci curvature or non-positive sectional curvature. As its applications, we establish some Picard type theorems and five-value type theorems for algebroid functions under certain conditions.