Kuijlaars and Saff's conjecture for the planar Riesz-energy constant

Let $C_{s,d}$ be the asymptotic Riesz-energy constant defined, for $d\geq 2$, by

$$C_{s,d}=\lim_{N\to\infty}\frac{\mathcal{E}_s([0,1]^d;N)}{N^{1+s/d}}.$$

Here $\mathcal{E}_s([0,1]^d;N)$ denotes the optimal discrete Riesz $s$-energy of $N$ points in the unit cube, and $\operatorname{\zeta}_{\Lambda}$ denotes the Epstein zeta function of the planar hexagonal lattice $\Lambda$. Kuijlaars and Saff's conjecture. For $s>2$,

$$C_{s,2}=\left(\frac{\sqrt{3}}{2}\right)^{s/2}\operatorname{\zeta}_{\Lambda}(s).$$

The constant is connected to sphere-packing density, and its precise value is open in dimensions $d\geq 2$; the conjecture specifies it in dimension two.