Metrical Diophantine approximation for quaternions

Abstract

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

30 pages. Some minor improvements

References in corpus (3)

• Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions
• Ubiquity and a general logarithm law for geodesics
• Diophantine approximation, Khintchine's theorem, torus geometry and Hausdorff dimension

Cited by in corpus (1)

• A Shrinking Target Problem with Target at Infinity in Rank One Homogeneous Spaces