Title: On Equilibrium Points of Logarithmic and Newtonian Potentials
Abstract: Let f(z) = ∑ j − 1 ∞ a j / ( z − z j ) and ∑ j − 1 ∞ | a j | / | z j | < ∞ . Then f can be realized as the complex conjugate of the gradient of a logarithmic potential or, for integral aj, as the logarithmic derivative of a meromorphic function. We investigate conditions on aj and zj that guarantee that f has zeros. In the potential theoretic setting, this asks whether certain logarithmic potentials with discrete mass distribution have equilibrium points.