Sums of distances between points of a sphere

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Abstract
Given N points on a unit sphere in k + 1 dimensional Euclidean space, we obtain an upper bound for the sum of all the distances they determine which improves upon earlier work by K. B. Stolarsky when k is even. We use his method, but derive a variant of W. M. Schmidt′s results for the discrepancy of spherical caps which is more suited to the present application.

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