Annals of Mathematics· 2017Q1
The sphere packing problem in dimension $24$
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- 2017year
Short summary
The Leech lattice is proven to be the densest packing of congruent spheres in 24 dimensions, and the unique optimal periodic packing.
AI-generated from the title and abstract; the full text is not read.
Key points
- The Leech lattice is the densest packing of congruent spheres in 24 dimensions.
- The Leech lattice is the unique optimal periodic packing in 24 dimensions.
- An optimal auxiliary function, analogous to Viazovska's for 8D, was developed.
- This work extends solutions for the sphere packing problem to higher dimensions.
AI-generated from the title and abstract; the full text is not read.
Abstract
Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.
The authors' abstract, as published at the source. Annals of Mathematics, 2017 · DOI ↗
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Field: Numerical Analysis
Numerical AnalysisMathematics