Nevanlinna characteristic

Summary

The Nevanlinna characteristic $T(r, f)$ of a meromorphic function $f$ on $\C$ measures its growth on the disc of radius $r$. It adds a term for the size of $f$ on the circle $\abs{z} = r$ and a term that counts the poles inside. For entire functions it plays the role of $\log M(r)$, and for meromorphic functions it replaces the degree of a rational function. It is the central quantity of Nevanlinna theory.