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We prove a conjecture of Ambrus, Ball and Erdélyi that equally spaced points maximize the minimum of discrete potentials on the unit circle whenever the potential is of the form $$\begin{aligned} \sum _{k=1}^n f(d(z,z_k)), \end{aligned}$$∑k=1nf(d(z,zk)),where $$f:[0,\pi ]\rightarrow [0,\infty ]$$f:[0,π]→[0,∞] is non-increasing and convex and $$d(z,w)$$d(z,w) denotes the geodesic distance between z and w on the circle.

Polarization Optimality of Equally Spaced Points on the Circle for Discrete Potentials