Meromorphic functions of the form $f(z) = \sum_{n=1}^\infty a_n/(z - z_n)$

Abstract

We prove some results on the zeros of functions of the form $f(z) = \sum_{n=1}^\infty \frac{a_n}{z - z_n}$, with complex $a_n$, using quasiconformal surgery, Fourier series methods, and Baernstein's spread theorem. Our results have applications to fixpoints of entire functions.