3 problems

Fix a dimension $d\geq 3$, density $\rho=1$, and $\alpha>0$. For the potential $p(r)=e^{-\alpha r^2}$, consider the optimal linear programming bound $\widehat{f}(0)-f(0)$ from the…

Let $f(t)=e^{-\alpha t^2}$, with $0<\alpha<\pi e$. For configurations of density $\rho$ in $\mathbb{R}^n$, let the minimal $f$-energy be the infimum of the corresponding Gaussian p…

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…