Diophantine properties of continued fractions on the Heisenberg group

Abstract

We provide several results on the diophantine properties of continued fractions on the Heisenberg group, many of which are analogous to classical results for real continued fractions. In particular, we show an analog of Khinchin's theorem and that convergents are also best approximants up to a constant factor of the denominator.

14 pages

Cited by in corpus (2)

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• Hausdorff dimension of limsup sets of rectangles in the Heisenberg group