International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 4, Pages 707-714
doi:10.1155/S0161171282000647

Sums of distances between points of a sphere

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.