In [ 3] we considered energy minimization of pair potentials among periodic sets of a fixed-point density. For a large class of potentials we presented sufficient conditions for a point lattice to give a local optimum among periodic sets. We hereby, in particular, derived a local version of Cohn and Kumar’s conjecture [ 1, Conjecture 9.4] by which the hexagonal lattice |$\textsf{A}_2$|⁠, the root lattice |$\textsf{E}_8$|⁠, and the Leech lattice are globally universally optimal. Latter conjecture has recently been proved for |$\textsf{E}_8$| and the Leech lattice by Cohn et al. [ 2].

中文翻译：

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勘误表：能量最小化，周期集和球形设计

在[ 3]我们考虑了定点密度的周期性集合中对电位的能量最小化。对于一大类电位，我们为点晶格提供了充分的条件，以在周期集中给出局部最优。特别是，我们据此推导了Cohn和Kumar猜想的本地版本[[1，Conjecture 9.4]中的六边形格子| $ \ textsf {A} _2 $ |⁠，根格子| $ \ textsf {E} _8 $ |⁠和Leech格子在全局范围内是最优的。| $ \ textsf {E} _8 $ |的最新猜想最近得到证明。和科恩等人的水ch晶格。[2]。