The Conway-Sloane tetralattice pairs are non-isometric

Details The Conway-Sloane tetralattice pairs are non-isometric The Conway-Sloane tetralattice pairs are non-isometric

2009-10-12

arxiv.org/abs/0910.2127v1

Mathematics

Number Theory

10 pages

Scientific paper

Conway and Sloane constructed a 4-parameter family of pairs of isospectral
lattices of rank four. They conjectured that all pairs in their family are
non-isometric, whenever the parameters are pairwise different, and verified
this for classical integral lattices of determinant up to $10^4$. In this
paper, we use our theory of lattice invariants to prove this conjecture.

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