ON EQUILIBRIUM POINTS OF LOGARITHMIC AND NEWTONIAN POTENTIALS

Let f(z) = SIGMA(j=1)infinity a(j)/(z-z(j)), where z(j) not-equal 0 an d Sigma(j-1)infinity \a(j)\/\z(j)\ < infinity). Then f can be realized as the complex conjugate of the gradient of a logarithmic potential o r, for integral a(j), as the logarithmic derivative of a meromorphic f unction. We investigate conditions on a(j) and z(j) that guarantee tha t f has zeros. In the potential theoretic setting, this asks whether c ertain logarithmic potentials with discrete mass distribution have equ ilibrium points.