On a property of 2-dimensional integral Euclidean lattices

Abstract

Let $L$ be any integral lattice in the 2-dimensional Euclidean space. Generalizing the earlier works of Hiroshi Maehara and others, we prove that for every integer $n>0$, there is a circle in the plane ${\mathbb{R}}^2$ that passes through exactly $n$ points of $L$.

arXiv comment9 pages