Sums of distances between points on a sphere. II

Stolarsky, Kenneth B.

doi:10.1090/S0002-9939-1973-0333995-9

Sums of distances between points on a sphere. II

Author: Kenneth B. Stolarsky
Journal: Proc. Amer. Math. Soc. 41 (1973), 575-582
MSC: Primary 52A40
DOI: https://doi.org/10.1090/S0002-9939-1973-0333995-9
MathSciNet review: 0333995
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Abstract: Given points on a unit sphere in Euclidean space, $m \geqq 2$ , 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 $m \geqq 5$ 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.

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