Approximation to points in the plane by SL(2,Z)-orbits

Abstract

Let x be a point in R^2 with irrational slope and let Γdenote the lattice SL(2,Z) acting linearly on R^2. Then, the orbit Γx is dense in R^2. We give efective results on the approximation of a point y in R^2 by points of the form γx, where γbelongs to Γ, in terms of the size of γ.

Cited by in corpus (3)

• Classifying orbits of the affine group over the integers
• The Bloch-Okounkov theorem for congruence subgroups and Taylor coefficients of quasi-Jacobi forms
• Inhomogeneous Diophantine approximation over fields of formal power series