Selected Applications of Nevanlinna Theory

Abstract

The present chapter is devoted to applications of Nevanlinna Theory to general questions in the theory of entire and meromorphic functions. This concerns algebraic differential and functional equations, uniqueness of meromorphic functions, and the value distribution of differential polynomials. We will always consider meromorphic functions in the plane, though more or less all results remain true if meromorphic functions on some punctured neighbourhood of infinity are considered. We have tried to avoid too much overlap with the books of Hayman (Meromorphic functions. Oxford University Press, Oxford, 1964), Laine (Nevanlinna theory and complex differential equations. De Gruyter studies in mathematics, vol 15. De Gruyter, Boston, 1993), and Wittich (Neuere Untersuchungen uber eindeutige Analytische Funktionen. Springer, Berlin, 1968), nevertheless we will present the basic results in the first section.