4 problems

Let $\Lambda$ be a Leech lattice in phase space of dimension $24$, with arbitrary fixed density greater than $1$. The Leech-lattice conjecture. There exists a Leech lattice that so…

Let $T_{[abc]}$ be a lattice in the notation of the paper, and let $W$ be a frame lattice corresponding to $T_{[abc]}$. A root is a lattice vector of minimal norm as defined in the…

Let $\Lambda$ be the Leech lattice, let $O(\Lambda)$ be its isometry group, and let $\Lambda_g$ denote the sublattice orthogonal to the fixed-point sublattice of $g\in O(\Lambda)$.…

E8 and Leech limiting-ratio conjecture. In the $E_8$ case,