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Tables of integral unimodular lattices constructed as \(k\)-neighbors in \(\mathbb{Z}^n\). (Tables de réseaux entiers unimodulaires construits comme \(k\)-voisins de \(\mathbb{Z}^n\).) (French) Zbl 0906.11033
Two lattices \(L\) and \(M\) on euclidean \({\mathbb R}^n\) are said to be \(k\)-neighbors for some positive integer \(k\) if both \(L/(L\cap M)\) and \(M/(L\cap M)\) are cyclic groups of order \(k\). The integral \(k\)-neighbors of the standard lattice \({\mathbb Z}^n\) represent all classes of self-dual lattices (the proof is sketched). In the tables published here one can find such a description for any class up to \(n=24\), together with some information related to the enumeration of these lattices in [J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups. 2nd ed. (1993; Zbl 0785.11036)].

11H06 Lattices and convex bodies (number-theoretic aspects)
11E12 Quadratic forms over global rings and fields
11-04 Software, source code, etc. for problems pertaining to number theory
Zbl 0785.11036
Full Text: DOI Numdam EuDML EMIS
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[2] Conway, J.H. et Sloane, N.J.A., Sphere Packings, Lattices and Groups, Springer, 1988. · Zbl 0634.52002
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[5] Schulze-Pillot, R., An algorithm for computing genera of ternary and quaternary quadratic forms, Proceedings of the International Symposium on Symbolic and Algebraic Computation, Bonn (1991), 134-143. · Zbl 0925.11045
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