On minima of sum of theta functions and Mueller-Ho Conjecture

Senping Luo, Juncheng Wei

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