Abstract:
The cube is the Dirichlet–Voronoi cell of the integer lattice $Z^n$.
We study the family of $(n+1)$-dimensional lattices $L_Z^{n+1}(h)$
obtained by superposition of layers of the lattice $Z^n$ and depending on
the distance $h$ between the layers. The quadratic forms
corresponding to these lattices generate a family of forms $f_h$.
If $h$ varies from 0 to infinity, the forms $f_h$ pierce the cone of positive quadratic forms
from one its boundary to another boundary and pass through a series of edge-forms.
Keywords:cubic lattice, superposition of layers, Dirichlet–Voronoi cells.
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