Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

2008/09/23 by Dzmitry Badziahin, Badziahin, Dzmitry
Mathematics · Physics and Astronomy · #11J13 #11J83 #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories #math.NT #msc:11J13 #msc:11J83

paper · pdf · doi:10.48550/arxiv.0809.3937

28 pages

arxiv created 2008/09/23 · openalex publication_date 2008/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in Rⁿ akin to the well established homogeneous theory. More specifically, the measure theoretic results obtained generalize the fundamental homogeneous theorems of R.C. Baker (1978), Dodson, Dickinson (2000) and Beresnevich, Bernik, Kleinbock, Margulis (2002). In the case of planar curves, the complete Hausdorff dimension theory is developed

Citations

• Fractal Geometry: Mathematical Foundations and Applications.
• Simultaneous inhomogeneous Diophantine approximation on manifolds

Related

• Diophantine approximation on planar curves and the distribution of rational points
• Diophantine approximation on curves
• A note on simultaneous Diophantine approximation on planar curves
• Hausdorff theory of dual approximation on planar curves
• Hausdorff Dimension and Diophantine Approximation