Good evening,
I need a reference for the topic I briefly describe here: let $\sigma$ be the Weierstrass $\sigma$-function, that is \begin{equation} \sigma(z):=z\prod_{m^2+n^2\neq0}\left(1-\frac{z}{m+in}\right)\exp\left(\frac{z}{m+in}+\frac{1}{2}\frac{z^2}{(m+in)^2}\right). \end{equation} Then, given a lattice of $\mathbb{C}^n$, say $L=A\mathbb{Z}^{2n}\subseteq\mathbb{C}^n$ ($A\in GL(n,\mathbb{C})$), one can modify the Weierstrass $\sigma$-function in order for it to vanish on $L$, that is \begin{equation} \sigma_L(z):=\sigma(A^{-1}z). \end{equation} One can prove that there exists $C>0$ such that for all $z\in\mathbb{C}$ \begin{equation} |\sigma_L(z)|\leq Ce^{\frac{\pi}{2}\Vert A^{-1}\Vert_{op}^2|z|^2}, \end{equation} being $\Vert A^{-1}\Vert_{op}=\sup_{|x|=1}|Ax|$ (the largest singular value of $A$), $|w|$ denoting both the modulus of $w$ or the $\ell^2$ norm of it when $w$ is a complex number or a $\mathbb{C}^n$ vector.
The issue is that of finding a representative matrix $A$ for the lattice $L$ which minimizes $\Vert A^{-1}\Vert_{op}$.
As Grochenig states (see his paper "Multivariate Gabor frames and sampling of entire functions of several variables"), this problem is strictly related to that of finding short vectors in a lattice or a basis consisting of short vectors. He refers to Cohen's work "A course in Computational Algebraic Number Theory", but I cannot find the point where he talks about this topic (actually, the book is pretty long, so I wonder if anyone that knows that work better than me could help me). Otherwise, any reference would be appreciated.