Geodesic
Superposition of layers of cubic lattice
Izvestiya. Mathematics , Tome 88 (2024) no. 6, pp. 1138-1153

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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. 
@article{IM2_2024_88_6_a5,
     author = {V. P. Grishukhin},
     title = {Superposition of layers of cubic lattice},
     journal = {Izvestiya. Mathematics },
     pages = {1138--1153},
     publisher = {mathdoc},
     volume = {88},
     number = {6},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2024_88_6_a5/}
}
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V. P. Grishukhin. Superposition of layers of cubic lattice. Izvestiya. Mathematics , Tome 88 (2024) no. 6, pp. 1138-1153. http://geodesic.mathdoc.fr/item/IM2_2024_88_6_a5/