Sums of Distances Between Points on a Sphere. II
- 1 December 1973
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 41 (2) , 575-582
- https://doi.org/10.2307/2039137
Abstract
Given points on a unit sphere in Euclidean space, , we show that the sum of all distances which they determine plus their discrepancy is a constant. As applications we obtain (i) an upper bound for the sum of the distances which for is smaller than any previously known and (ii) the existence of point distributions with small discrepancy. We make use of W. M. Schmidt's work on the discrepancy of spherical caps.Keywords
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