7 problems

Let $\Lambda$ be a lattice in three-dimensional Euclidean space, and for $s>3$ define its Epstein zeta function by … The FCC lattice denotes the face-centered cubic lattice. Sarnak…

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…

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 $\zeta_L$ 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,…

Let $b6_3(S,s)$ denote the Epstein zeta function associated with a three-dimensional lattice $S$, and let FCC and BCC denote the face-centered-cubic and body-centered-cubic lattice…

Hexagonal-lattice energy conjecture.

Let $\Lambda$ be a lattice and define its Epstein zeta function, for $s>0$, by … where $\mathbf{p}$ ranges over the nonzero lattice vectors of $\Lambda$. A lattice packing is maxim…