48 dimensional even unimodular nearly extremal lattices.

Abstract

In this paper we introduce the notion of an even unimodular nearly extremal lattice in the case of 48 dimension. We prove two basic properties of such lattices $L$. First we prove that any nearly extremal lattice $L$ is generated by the vectors of norm 4 and norm 6 in $L$. Next we prove that the Siegel theta series of degree 2 associated with an even unimodular nearly extremal lattice is determined by the Fourier coefficients which are connected with the vectors of norm 4.