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

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

2010-04-08

arxiv.org/abs/1004.1326v1

Mathematics

Number Theory

Scientific paper

Let x be a point in R^2 with irrational slope and let \Gamma denote the
lattice SL(2,Z) acting linearly on R^2. Then, the orbit \Gamma x is dense in
R^2. We give efective results on the approximation of a point y in R^2 by
points of the form \gamma x, where \gamma belongs to \Gamma, in terms of the
size of \gamma.

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