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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