7 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 the face-centered cubic and body-centered cubic lattices in ${\mathbb R}^3$ be scaled to the specified density $\rho$, and let the potential be $r \mapsto e^{-\pi r^2}$. Gaussi…

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…

Let $\varphi(x)=e^{-c|x|^2}$ with $c>0$, and construct admissible auxiliary functions $h$ by taking a radial polynomial times $e^{-\pi|x|^2}$, with double roots at the modified roo…

Let $V$ be a generalized Gaussian potential whose covariance function $\gamma$ is defined pointwise, continuous on $\mathbb{R}^d\setminus\\{0\\}$, satisfies $\gamma(0)=\infty$, and…

Köksal's analytical-energy conjecture. The main idea of the proposed approximation is embodied in