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

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. 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.