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In this paper we investigate greedy energy sequences on the unit circle for the logarithmic and Riesz potentials. By definition, if (an) ∞ n=0 is a greedy s-energy sequence on the unit circle, the Riesz potential UN,s(x) := N−1 k=0 |a k − x| −s , s > 0, generated by the first N points of the sequence attains its minimum value on the circle at the point aN . In this work, we analyze the asymptotic properties of these extremal values UN,s(aN ), treating separately the cases 0 < s < 1, s = 1, and s > 1. We present new second-order asymptotic formulas for UN,s(aN ) in the cases 0 < s < 1 and s = 1. A first-order result for s > 1 is proved, and it is shown that the first-order normalized sequence (UN,s(aN )/N s ) ∞ N=1 is divergent in this case.

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