Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3)

TL;DR

This paper extends the understanding of extremal even unimodular lattices of ranks 40, 80, and 120, showing they are generated by vectors of specific norms, building on previous work for rank 40.

Contribution

It generalizes Ozeki's result for rank 40 to higher ranks 80 and 120, identifying the generating vectors for these lattices.

Findings

Lattices of rank 40r are generated by vectors of norms 4r and 4r+2

Extension of Ozeki's result from rank 40 to ranks 80 and 120

Provides structural insight into extremal even unimodular lattices

Abstract

We show that if L is an extremal even unimodular lattice of rank 40r with r=1,2,3 then L is generated by its vectors of norms 4r and 4r+2. Our result is an extension of Ozeki's result for the case r=1.