Mathematics — Number Theory · quadratic-fields-ideals-lattices
Problem
Show that the norm N(L) of a lattice L in RΔ can be computed in the following way. Choose a basis α,β for L and let Pα,β be the parallelogram with vertices 0, α, β, and α+β. Then N(L) is the total number of points of RΔ in the interior of Pα,β plus the number of points of RΔ in the interiors of two adjacent edges of Pα,β, plus an additional 1 for the vertex of Pα,β between these two edges.