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On the zeros of meromorphic functions of the formf(z)=Σ ∞ k=1 a k/z−z k

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Abstract

We study the zero distribution of meromorphic functions of the formf(z)=Σ ∞ k=1 a k/z−z k wherea k >0. Noting thatf is the complex conjugate of the gradient of a logarithmic potential, our results have application in the study of the equilibrium points of such a potential.

Furthermore, answering a question of Hayman, we also show that the derivative of a meromorphic function of order at most one, minimal type has infinitely many zeros.

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Authors and Affiliations

  1. Department of Mathematics, Puruue University, 47907, Lafayette, IN, USA

    Alexandre Eremenko

  2. Department of Mathematics, University of Nottingham, England

    Jim Langley

  3. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA

    John Rossi

Authors
  1. Alexandre Eremenko
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  2. Jim Langley
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  3. John Rossi
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Additional information

Supported by an NSF grant.

Research carried out during a visit to the University of Illinois, funded by an NSF grant.

Research carried out at the University of York while serving as a British Science and Engineering Research Council (SERC) fellow. The author gratefully acknowledges the hospitality and support extended to him by the Department of Mathematics.

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Eremenko, A., Langley, J. & Rossi, J. On the zeros of meromorphic functions of the formf(z)=Σ ∞ k=1 a k/z−z k . J. Anal. Math. 62, 271–286 (1994). https://doi.org/10.1007/BF02835958

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  • DOI: https://doi.org/10.1007/BF02835958

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