Metrical Diophantine approximation for quaternions

2011/09/30 by M. M. Dodson, Maurice Dodson, Brent Everitt
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebra over a field #Computer science #Diophantine approximation #Diophantine equation #Diophantine set #Discrete mathematics #Geometry #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Mathematics #Measure (data warehouse) #Pure mathematics #Quaternion #math.NT

paper · pdf · doi:10.1017/s0305004114000462

published as Math. Proc. Camb. Phil. Soc. 157 (2014) 513-542 · 30 pages. Some minor improvements

arxiv created 2014/10/17 · openalex publication_date 2014/11/01 · arxiv updated 2019/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Abstract Analogues of the classical theorems of Khintchine, Jarník and Jarník-Besicovitch in the metrical theory of Diophantine approximation are established for quaternions by applying results on the measure of general ‘lim sup’ sets.

Citations

• Diophantine approximation, Khintchine's theorem, torus geometry and Hausdorff dimension
• Ubiquity and a general logarithm law for geodesics
• Hausdorff dimension and Diophantine approximation
• Ueber die angen�herte Darstellung der Irrationalzahlen durch rationale Br�che
• A Mass Transference Principle and the Duffin–Schaeffer conjecture for Hausdorff measures
• Geometric Measure Theory