Revista Matemática Iberoamericana

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Volume 20, Issue 1, 2004, pp. 285–314
DOI: 10.4171/RMI/390

Published online: 2004-04-30

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

James K. Langley[1] and John Rossi[2]

(1) University of Nottingham, UK
(2) Virginia Tech and State University, Blacksburg, USA

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.

Keywords: Meromorphic functions, zeros, critical points, logarithmic potentials, quasiconformal surgery

Langley James, Rossi John: Meromorphic functions of the form $f(z) = \sum_{n=1}^\infty a_n/(z - z_n)$. Rev. Mat. Iberoam. 20 (2004), 285-314. doi: 10.4171/RMI/390