## Abstract

The Cohn-Kumar conjecture states that the triangular lattice in dimension 2, the E_{8} lattice in dimension 8, and the Leech lattice in dimension 24 are universally minimizing in the sense that they minimize the total pair interaction energy of infinite point configurations for all completely monotone functions of the squared distance. This conjecture was recently proved by Cohn-Kumar-Miller-Radchenko-Viazovska in dimensions 8 and 24. We explain in this note how the conjecture implies the minimality of the same lattices for the Coulomb and Riesz renormalized energies as well as jellium and periodic jellium energies, hence settling the question of their minimization in dimensions 8 and 24.

Original language | English (US) |
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Pages (from-to) | 3047-3057 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 148 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2020 |

## Keywords

- Abrikosov lattice
- Cohn-Kumar conjecture
- Coulomb interaction
- Crystallization
- Jellium
- Renormalized energy
- Riesz interaction
- Triangular lattice
- Wigner crystal

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics