- December 2015
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- Abstract In this paper we investigate the asymptotic behavior of the Riesz s-energy of the first N points of a greedy s-energy sequence on the unit circle, for all values of s in the range 0 ≤ s < ∞ (identifying as usual the case s = 0 with the logarithmic energy). In the context of the unit circle, greedy s-energy sequences coincide with the classical Leja sequences constructed using the logarithmic potential. We obtain first-order and second-order asymptotic results. The key idea is to express the Riesz s-energy of the first N points of a greedy s-energy sequence in terms of the binary representation of N. Motivated by our results, we pose some conjectures for general sequences on the unit circle.
- greedy energy sequence; leja sequence; riesz kernel; equilibrium; measure; optimal energy configuration