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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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