Dimension reduction techniques for the minimization of theta functions on lattices

Laurent Bétermin, Mircea Petrache

We consider the minimization of theta functions $\theta \_\Lambda (\alpha )=\sum \_p\in \Lambda e^{-\pi \alpha |p{|}^2}$ amongst lattices $\Lambda \subset {\mathbb{R}}^d$, by reducing the dimension of the problem, following as…