LeVeque type inequalities and discrepancy estimates for minimal energy configurations on spheres
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Let S{double-struck}d denote the unit sphere in the Euclidean space R{double-struck}d+1(d1). We develop LeVeque type inequalities for the discrepancy between the rotationally invariant probability measure and the normalized counting measures on S{double-struck}d. We obtain both upper bound and lower bound estimates. We then use these inequalities to estimate the discrepancy of the normalized counting measures associated with minimal energy configurations on S{double-struck}d. 2010 Elsevier Inc.