Two-dimensional lattices with few distances
Pieter Moree, Robert Osburn
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.
Create a lesson
Related papers
Almost primes in short intervals and averages of long Dirichlet polynomial approximations to (ζ'/ζ)k
Siegfred Baluyot, John Brian Conrey, Ayesha Irfan et al.
On the Diophantine equation Cx2+p12m1p22m2·s pk2mk=yq
Usha K. Sangale, Priyanka R. Satpute
Asymptotics for partitions over the Fibonacci numbers and related sequences, II
Michael Coons, Simon Kristensen, Mathias L. Laursen
Inverse powers and 2-adic properties of binary 3 x 3 matrices associated with the Tribonacci sequence
Wilson Arley Martinez, Samin Ingrith Ceron
Counting irreducible skew polynomials x2n+axn+1
Tomoya Hayata, Takahiro Tsushima
Finding Integer Roots of Polynomials in Nearly Optimal Time
Yansong Feng, Itamar Nir