This book offers a modern introduction to Nevanlinna theory and its intricate relation to the
theory of normal families algebraic functions asymptotic series and algebraic differential
equations. Following a comprehensive treatment of Nevanlinna's theory of value distribution
the author presents advances made since Hayman's work on the value distribution of differential
polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves
and Briot-Bouquet differential equations. In addition to discussing classical applications of
Nevanlinna theory the book outlines state-of-the-art research such as the effect of the
Yosida and Zalcman-Pang method of re-scaling to algebraic differential equations and presents
the Painlevé-Yosida theorem which relates Painlevé transcendents and solutions to selected 2D
Hamiltonian systems to certain Yosida classes of meromorphic functions. Aimed at graduate
students interested in recent developments in the field and researchers working on related
problems Nevanlinna Theory Normal Families and Algebraic Differential Equations will also be
of interest to complex analysts looking for an introduction to various topics in the subject
area. With examples exercises and proofs seamlessly intertwined with the body of the text
this book is particularly suitable for the more advanced reader.
