A note on Diophatine approximation in \rmSL₂(ℝ)

2013/04/17 by Nikolay Moshchevitin, Moshchevitin, Nikolay
Mathematics · #11H56 #11J70 #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT) #math.DS #math.NT #msc:11H56 #msc:11J70

paper · pdf · doi:10.48550/arxiv.1304.4842

5 pages

arxiv created 2013/04/17 · openalex publication_date 2013/04/17 · arxiv updated 2013/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a quantitative version of the following statement: the unipotent flow orbit of a typical lattice in \rmSL₂(ℝ)/\rmSL₂(ℤ) is dense. Our quantitative result uses A. Weil's bounds for Kloostermann sums.

Related

• A brief remark on orbits of SL(2,Z) in the euclidean plane
• Logarithm laws for unipotent flows, I
• Density of orbits of horocycle flows at sub-quadratic polynomial times
• On the rate of equidistribution of expanding horospheres in\n finite-volume quotients of \SL(2,\ℂ)
• Inhomogeneous approximation with coprime integers and lattice orbits