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We consider asymptotic properties of ground state configurations of point charges restricted to a conducting surface and interacting through an inverse power law potential as the number of points goes to infinity. Experimentally, it appears that the local structure of such configurations is almost everywhere hexagonal. We relate this to a conjecture that a certain constant appearing in the asymptotic expansion of the total energy is given by the Epstein zeta function on a hexagonal lattice. Host: Razvan Teodorescu, T-CNLS and T-13 |