Lattice points close to ovals, arcs, and helixes

Abstract: In 1972 Schinzel showed that the largest distance between three lattice points on a circle of radius $R$ is at least $\sqrt[3]{2} R^{1/3}$. We generalize Schinzel's result to ovals and arcs with bounded curvature in the plane and lattice points close to the curve. Furthermore, we extend the result to the case of affine lattices. Finally, we obtain similar results when the curve is a helix in three dimensional space.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)