The Coulomb energy of spherical designs on S 2

Consider a sequence of point sets on S, where each set X is a spherical ndesign with m points, where m = O(n), and where the spherical distance between points of X is at least λ/ √ m, for some λ common to all sets of the sequence. For each X of such a sequence, the Coulomb energy E(X) is bounded by E(X) 6 1 2 m2 + O(m). The first term and the order of the second term are the same as for the bounds given by conjectures on the minimum energy for point sets on S. We give reasons for considering spherical designs, justify the restriction on spherical distance between points, and outline the method of estimation used to obtain the energy bound. This is joint work with Kerstin Hesse.