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20112025
most citedOn the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target

3 citations · 3 across the 10 of their papers we have counts for

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math.NT2022

Convergence of improper Iwasawa Continued Fractions

Anton Lukyanenko, Joseph Vandehey

We prove the convergence of a wide class of continued fractions, including generalized continued fractions over quaternions and octonions. Fractional points in these systems are no…

math.NT2015

Intrinsic Diophantine approximation in Carnot groups and in the Siegel model of the Heisenberg group

Anton Lukyanenko, Joseph Vandehey

We initiate the study of an intrinsic notion of Diophantine approximation on a rational Carnot group . If has Hausdorff dimension , we show that its Diophantine exponent…

math.NT2013

Continued fractions on the Heisenberg group

Anton Lukyanenko, Joseph Vandehey

We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several…