Revista Matemática Iberoamericana

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

James K. Langley and John Rossi

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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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 20, Number 1 (2004), 285-314.

Dates
First available in Project Euclid: 2 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1080928430

Mathematical Reviews number (MathSciNet)
MR2076782

Zentralblatt MATH identifier
1061.30022

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory

Keywords
meromorphic functions zeros critical points logarithmic potentials quasiconformal surgery

Citation

Langley, James K.; Rossi, John. Meromorphic functions of the form $f(z) = \sum_{n=1}^\infty a_n/(z - z_n)$. Rev. Mat. Iberoamericana 20 (2004), no. 1, 285--314. https://projecteuclid.org/euclid.rmi/1080928430


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