Two-dimensional lattices with few distances

Details Two-dimensional lattices with few distances Two-dimensional lattices with few distances

2006-04-07

arxiv.org/abs/math/0604163v2

Enseignement Math. 52 (2006), 361-380

Mathematics

Number Theory

21 pages, final version, accepted for publication in L'Enseignement Math\'ematique

Scientific paper

We prove that of all two-dimensional lattices of covolume 1 the hexagonal
lattice has asymptotically the fewest distances. An analogous result for
dimensions 3 to 8 was proved in 1991 by Conway and Sloane. Moreover, we give a
survey of some related literature, in particular progress on a conjecture from
1995 due to Schmutz Schaller.

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