On Minima of Difference of Epstein Zeta Functions and Exact Solutions to Lennard-Jones Lattice Energy

Senping Luo, Juncheng Wei

Let $\zeta (s,z)={\sum }_{(m,n)\in {\mathbb{Z}}^2\backslash \{0\}}\frac{(\Im (z){)}^s}{|mz+n{|}^{2s}}$ be the Eisenstein series/Epstein Zeta function. Motivated by widely used Lennard-Jones potenti…