A simple proof of a reverse Minkowski theorem for integral lattices

2023/06/06 by Regev, Oded, Stephens-Davidowitz, Noah · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2306.03697

Abstract

We prove that for any integral lattice L ⊂ ℝⁿ (that is, a lattice L such that the inner product ⟨ y₁,y₂ ⟩ is an integer for all y₁, y₂ ∈ L) and any positive integer k, |\ y ∈ L : ‖y‖² = k\| ≤ 2 \binomn+2k-22k-1 , giving a nearly tight reverse Minkowski theorem for integral lattices.

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