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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 Lukyanenko, and Joseph Vandehey. "Continued fractions on the Heisenberg group." Acta Arithmetica 167.1 (2015): 19-42. <http://eudml.org/doc/279141>.
@article{AntonLukyanenko2015, abstract = {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.}, author = {Anton Lukyanenko, Joseph Vandehey}, journal = {Acta Arithmetica}, keywords = {continued fractions; Heisenberg group}, language = {eng}, number = {1}, pages = {19-42}, title = {Continued fractions on the Heisenberg group}, url = {http://eudml.org/doc/279141}, volume = {167}, year = {2015}, }
TY - JOUR AU - Anton Lukyanenko AU - Joseph Vandehey TI - Continued fractions on the Heisenberg group JO - Acta Arithmetica PY - 2015 VL - 167 IS - 1 SP - 19 EP - 42 AB - 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. LA - eng KW - continued fractions; Heisenberg group UR - http://eudml.org/doc/279141 ER -