A method for finding a minimal point of the lattice in cubic number fields

Kan Kaneko
2014 Tsukuba Journal of Mathematics  
Proposition 1.2. Let R be a reduced lattice of K, and let L := R τ . Then there exists a Proof. Let R = 〈1, β, γ〉. For ε > 0, we shall consider a rectangular neighbourhood of (0, 0), i.e. W (ε, √ 3/2) = {(u, v) ∈ R 2 ; |u| < ε, |v| < √ 3/2}. By Minkowski's convex body theorem,
doi:10.21099/tkbjm/1407938674 fatcat:yplxe7xpe5fv3aljjvxw7kigsa