Examples of even unimodular extremal lattices of rank 40 and their Siegel theta-series of degree 2
An even unimodular lattice in n-dimensional Euclidean space is called extremal if its minimum attains the upper bound \(2[n/24]+2;\) all such lattices have the same theta series of degree 1. One knows that for \(n=40\) there are more than \(10^{50}\) classes of extremal lattices [\textit{M. Peters}, Bull. Lond. Math. Soc. 15, 18-20 (1983; Zbl 0506.10016)]. In the present paper three of these are found to have different Siegel theta series of degree 2, and the question is posed whether all the classes can be distinguished in this way.
scientific article; zbMATH DE number 4040003