4 problems

Let $C_{s,d}$ be the asymptotic Riesz $s$-energy constant for $d$-rectifiable sets, and let … be the Epstein zeta function of a lattice $\Lambda\subset\mathbb{R}^d$ with covolume…

A lattice quantizer is a lattice in Euclidean space whose normalized second moment measures its mean square quantization error at fixed point density. The packing problem asks for…

Let $\Delta_d$ denote the largest sphere-packing density in $\mathbb{R}^d$. In dimensions $d=4,5,6,7$, suppose the conjectured lattice-packing values of $\Delta_d$ are used to eval…

Let $\{z_j\}_1^n$ be the system of particles in the $\beta$-ensemble, and suppose the conditions of the corollary hold: $c<1/(8\sqrt{e})$, together with the regularity condition…