Two-dimensional lattices with few distances

Pieter Moree; Robert Osburn

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Two-dimensional lattices with few distances

Pieter Moree·Robert Osburn

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Abstract

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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Pieter Moree, Robert Osburn. 2006-10-20. Two-dimensional lattices with few distances. https://arxiv.org/abs/math/0604163

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