3 problems

Optimality conjecture for triangular and square lattices. There exist $1<p_1<p_2$ and $1<p_3<p_4$ such that, up to rotation, the following hold:

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…

Let $\zeta_L$ and $\theta_L$ denote the Epstein zeta function and theta function of a Bravais lattice $L$, and let $D_3$ and $D_3^*$ denote the FCC and BCC lattices, respectively,…