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

### James K. Langley

University of Nottingham, UK### John Rossi

Virginia Tech and State University, Blacksburg, USA

## 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.

## Cite this article

James K. Langley, John Rossi, Meromorphic functions of the form $f(z) = \sum_{n=1}^\infty a_n/(z - z_n)$. Rev. Mat. Iberoam. 20 (2004), no. 1, pp. 285–314

DOI 10.4171/RMI/390