Fekete problem

In mathematics, the Fekete problem is, given a natural number N and a real s ≥ 0, to find the points x₁,...,x_N on the 2-sphere for which the s-energy, defined by

for s > 0 and by

for s = 0, is minimal. For s > 0, such points are called s-Fekete points, and for s = 0, logarithmic Fekete points (see ). More generally, one can consider the same problem on the d-dimensional sphere, or on a Riemannian manifold (in which case ||x_i −x_j|| is replaced with the Riemannian distance between x_i and x_j).

The problem originated in the paper by who considered the one-dimensional, s = 0 case, answering a question of Issai Schur.

An algorithmic version of the Fekete problem is number 7 on the list of problems discussed by .

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