JournalsrmiVol. 20, No. 1pp. 285–314

Meromorphic functions of the form f(z)=∑n=1∞an/(z−zn)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)=∑n=1∞anz−znf(z) = \sum_{n=1}^\infty \frac{a_n}{z - z_n}, with complex ana_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)=∑n=1∞an/(z−zn)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