Minima of odd unimodular lattices in dimension \(24m\)
The following theorem is proved: Suppose that \(L\) is a unimodular \(\mathbb{Z}\)-lattice in dimension \(n=24k\). Suppose further that the minimum \(\mu(L)= 2k+2\). Then \(L\) must be an even lattice. Since Rains and Sloane showed \(\mu(L)\leq 2k+2\), this gives new bounds for odd unimodular lattices in dimension \(24k\).
scientific article; zbMATH DE number 1787788
scientific article