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arXiv · 2608.22590

On the constant in Klartag's theorem for lattice packings in high dimensions

Irina Rezvyakova
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Abstract

In 2025, Boaz Klartag proved that there exists a lattice sphere packing in $\mathbb{R}^n$ whose density is at least \[ c n^2 2^{-n}, \] where $c>0$ is an absolute constant. Our aim is to refine the analysis of Klartag's argument and to show that the constant can be taken as \[ c = \frac{1}{2e} - o(1), \qquad n\to\infty. \]

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Irina Rezvyakova. 2026-08-23. On the constant in Klartag's theorem for lattice packings in high dimensions. https://arxiv.org/abs/2608.22590

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