English

Approximation of points in the plane by generic lattice orbits

Number Theory 2016-06-29 v1

Abstract

We give upper and lower bounds for Diophantine exponents measuring how well a point in the plane can be approximated by points in the orbit of a lattice Γ<SL2(R)\Gamma<\mathrm{SL}_2(\mathbb{R}) acting linearly on R2\mathbb{R}^2. Our method gives bounds that are uniform for almost all orbits.

Keywords

Cite

@article{arxiv.1606.08540,
  title  = {Approximation of points in the plane by generic lattice orbits},
  author = {Dubi Kelmer},
  journal= {arXiv preprint arXiv:1606.08540},
  year   = {2016}
}
R2 v1 2026-06-22T14:36:06.317Z