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Continued fractions on the Heisenberg group

Volume 167 / 2015

Anton Lukyanenko, Joseph Vandehey Acta Arithmetica 167 (2015), 19-42 MSC: Primary 11J70; Secondary 22E40, 53C17. DOI: 10.4064/aa167-1-2


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 surprising analogs of classical formulas about continued fractions.


  • Anton LukyanenkoDepartment of Mathematics
    University of Michigan
    530 Church Street
    Ann Arbor, MI 48109, U.S.A.
  • Joseph VandeheyDepartment of Mathematics
    University of Georgia at Athens
    Athens, GA 30602, U.S.A.

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