6 problems

Let $\mathsf{E}_8$ denote the root lattice in dimension $8$. A globally optimal solution to the lattice packing-covering problem is one attaining the best packing-covering value am…

Let $\mathsf{E}_8$ denote the root lattice in dimension $8$. A lattice is a locally optimal solution to the lattice packing-covering problem if no sufficiently small deformation im…

For $\varepsilon\in\{0,1\}$, let … where $r^\varepsilon_{n,k}$ has degree at most $2k+\varepsilon$, is nonzero, vanishes at $2,4,\ldots,2k$, and is a linear combination of the rele…

Let $\varphi(x)=e^{-c|x|^2}$ in $\mathbb R^n$, where $n\in\{8,24\}$, and let $h$ be the limiting auxiliary function from the sharp energy-bound convergence conjecture. Let…

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

For each real parameter $n$ with $0<n<10$, define $f_k$ using forced roots at the vector lengths of the $E_8$ lattice, and let the associated limiting functions be those in the pre…