On the zeros of meromorphic functions of the formf(z)=Σ k=1 ∞ a k/z−z k
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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.
KeywordsEntire Function Meromorphic Function Straight Line Segment Subharmonic Function Level Curf
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- J. Clunie, A. Eremenko and J. Rossi,On the equilibrium points of logarithmic and Newtonian potentials, J. London Math. Soc. (to appear).Google Scholar
- A. Goldberg and I. Ostrovski,Distribution of Values of Meromorphic Functions, Moscow, Nauka, 1970 (Russian).Google Scholar
- W. Hayman,Multivalent Functions, Cambridge University Press, 1958.Google Scholar
- W. Hayman,Meromorphic Functions, Oxford University Press, 1964.Google Scholar
- W. Hayman,Subharmonic Functions II, Academic Press, London, 1989.Google Scholar