Upper bounds on spherical cap discrepancy of Riesz s-energy minimizers on S^d are obtained via Sobolev discrepancy estimates, improving prior results for 0 ≤ s < 2 (s ≠ 1) in S^2 and d-t0 < s < d (s ≠ d-1) when d ≥ 3.
Lang, Introduction to Arakelov Theory, Springer-Verlag New York, 1988
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Discrepancy of minimal Riesz energy points
Upper bounds on spherical cap discrepancy of Riesz s-energy minimizers on S^d are obtained via Sobolev discrepancy estimates, improving prior results for 0 ≤ s < 2 (s ≠ 1) in S^2 and d-t0 < s < d (s ≠ d-1) when d ≥ 3.