International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 4, Pages 707-714
Sums of distances between points of a sphere
Department of Mathematics, Royal Holloway College, Surrey, Egham TW20 OEX, UK
Received 1 February 1982
Copyright © 1982 Glyn Harman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Given points on a unit sphere in 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 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.