We study the zero distribution of meromorphic functions of the formf(z) = ~--]ff=l at where a t. > 0. Noting thatfts the complex conjugate of Z--Z k 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 mo...