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On Korkin-Zolotarev’s construction. (English. Russian original) Zbl 0827.11038
Discrete Math. Appl. 4, No. 2, 143-146 (1994); translation from Diskretn. Mat. 6, No. 1, 155-157 (1994).
Using the well-known lattice which was constructed by Korkin-Zolotarev (containing 240 minimal vectors) and applying an approach based on the positive definite functions on the Gegenbauer system, in this paper it is shown that the minimum of the potential energy of interactions of 240 unit charges placed on the sphere in \(\mathbb{R}^8\) is attained on the minimal vectors and it is equal to \({{637975} \over {72}}\).
Reviewer: R.Nehse (Ilmenau)

MSC:
11H55 Quadratic forms (reduction theory, extreme forms, etc.)
41A50 Best approximation, Chebyshev systems
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