Sums of distances between points of a sphere

[摘要] GivenNpoints on a unit sphere ink+1dimensional 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 whenkis 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.

[学科分类] 数学（综合）