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

Sums of distances between points of a sphere

Glyn Harman

Department of Mathematics, Royal Holloway College, Surrey, Egham TW20 OEX, UK

Received 1 February 1982

Copyright © 1982 Hindawi Publishing Corporation. 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.

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.