Topics in Nevanlinna theory - Buck, Matthew M. (2013)
Nevanlinna Theory is a powerful quantitative tool used to study the growth and behaviour of meromorphic functions on the complex plane. It plays an important role in value distribution theory, including generalising Picard's theorem that an entire function which omits two finite values is constant. The Nevanlinna Characteristic T(r,f) is a measure of a function's growth, and its associated counting function estimates how often certain values are taken. Using these tools, as well as other forms of modern complex analysis, we investigate several problems relating to differential polynomials in meromorphic functions. We also present a result relating to integer-valued meromorphic functions.