On the continued fractions of quadratic surds

David G. Cantor

Acta Arithmetica (1994)

  • Volume: 68, Issue: 4, page 295-305
  • ISSN: 0065-1036

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David G. Cantor. "On the continued fractions of quadratic surds." Acta Arithmetica 68.4 (1994): 295-305. <http://eudml.org/doc/206663>.

@article{DavidG1994,
author = {David G. Cantor},
journal = {Acta Arithmetica},
keywords = {continued fractions; surds; automata; quadratic surds; bounded partial quotients; formal Laurent series},
language = {eng},
number = {4},
pages = {295-305},
title = {On the continued fractions of quadratic surds},
url = {http://eudml.org/doc/206663},
volume = {68},
year = {1994},
}

TY - JOUR
AU - David G. Cantor
TI - On the continued fractions of quadratic surds
JO - Acta Arithmetica
PY - 1994
VL - 68
IS - 4
SP - 295
EP - 305
LA - eng
KW - continued fractions; surds; automata; quadratic surds; bounded partial quotients; formal Laurent series
UR - http://eudml.org/doc/206663
ER -

References

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  1. [1] J.-P. Allouche, M. Mendès France and A. J. van der Poorten, An infinite product with bounded partial quotients, Acta Arith. 59 (1991), 171-182. 
  2. [2] E. Artin, Quadratische Körper im Gebiet der höheren Kongruenzen I, II, in: The Collected Papers of Emil Artin, Addison-Wesley, 1965 (originally published in Math. Z. 19 (1924), 153-246). Zbl50.0107.01
  3. [3] L. E. Baum and M. M. Sweet, Continued fractions of algebraic power series in characteristic 2, Ann. of Math. 103 (1976), 593-610. Zbl0312.10024
  4. [4] L. E. Baum and M. M. Sweet, Badly approximable power series in characteristic 2, Ann. of Math. 105 (1977), 573-580. Zbl0352.10017
  5. [5] D. G. Cantor, Investigations of T-numbers and E-sequences, in: Computers in Number Theory, A. O. L. Atkin and B. J. Birch (eds.), Academic Press, 1971, 137-140. 
  6. [6] D. G. Cantor, On the analogue of the division polynomials for hyperelliptic curves, J. Reine Angew. Math. 447 (1994), 91-145. Zbl0788.14026
  7. [7] M. Mendès France and A. J. van der Poorten, Some explicit continued fraction expansions, Mathematika 38 (1991), 1-9. 
  8. [8] J. P. Mesirov and M. M. Sweet, Continued fraction expansions of rational expressions with irreducible denominators in characteristic 2, J. Number Theory 27 (1987), 144-148. Zbl0626.10029
  9. [9] W. H. Mills and D. P. Robbins, Continued fractions for certain algebraic power series, J. Number Theory 23 (1986), 388-404. Zbl0591.10021
  10. [10] J. Shallit, Real numbers with bounded partial quotients: A survey, Enseign. Math. 38 (1992), 151-187. Zbl0753.11006
  11. [11] A. J. van der Poorten, Fractions of the period of the continued fraction expansion of quadratic integers, Bull. Austral. Math. Soc. 44 (1991), 155-169. Zbl0733.11004
  12. [12] A. J. van der Poorten and J. Shallit, Folded continued fractions, J. Number Theory 40 (1992), 237-250. Zbl0753.11005

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