This book describes the theories and developments in Nevanlinna
theory and Diophantine approximation. Although these two subjects
belong to the different areas: one in complex analysis and one in
number theory, it has been discovered that a number of striking
similarities exist between these two subjects. A growing
understanding of these connections has led to significant advances
in both fields. Outstanding conjectures from decades ago are being
solved.Over the past 20 years since the first edition appeared,
there have been many new and significant developments. The new
edition greatly expands the materials. In addition, three new
chapters were added. In particular, the theory of algebraic curves,
as well as the algebraic hyperbolicity, which provided the
motivation for the Nevanlinna theory.
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