Continued fraction expansions for complex numbers-a general approach

S. G. Dani. "Continued fraction expansions for complex numbers-a general approach." Acta Arithmetica 171.4 (2015): 355-369. <http://eudml.org/doc/279347>.

@article{S2015,
abstract = {We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the absolute values of the denominators of the convergents for a class of continued fraction algorithms with partial quotients in the ring of Eisenstein integers.},
author = {S. G. Dani},
journal = {Acta Arithmetica},
keywords = {continued fraction expansions of complex numbers; algorithms; Eisenstein integers; Lagrange theorem; growth of denominators of convergents},
language = {eng},
number = {4},
pages = {355-369},
title = {Continued fraction expansions for complex numbers-a general approach},
url = {http://eudml.org/doc/279347},
volume = {171},
year = {2015},
}

TY - JOUR
AU - S. G. Dani
TI - Continued fraction expansions for complex numbers-a general approach
JO - Acta Arithmetica
PY - 2015
VL - 171
IS - 4
SP - 355
EP - 369
AB - We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the absolute values of the denominators of the convergents for a class of continued fraction algorithms with partial quotients in the ring of Eisenstein integers.
LA - eng
KW - continued fraction expansions of complex numbers; algorithms; Eisenstein integers; Lagrange theorem; growth of denominators of convergents
UR - http://eudml.org/doc/279347
ER -