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

James K. Langley; John Rossi

doi:10.4171/rmi/390

JournalsrmiVol. 20, No. 1pp. 285–314

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

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

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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.

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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