On minima of difference of theta functions and application to hexagonal crystallization

Senping Luo, Juncheng Wei

Let $z=x+iy\in \mathbb{H}:=\{z=x+iy\in \mathbb{C}:y>0\}$ and $\theta (\alpha ;z)={\sum }_{(m,n)\in {\mathbb{Z}}^2}{e}^{-\alpha \frac{\pi }{y}|mz+n{|}^2}$ be the theta function associated with the lattice…