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ArticleOriginal scientific text

Title

On the continued fractions of quadratic surds

Authors 1

Affiliations

  1. Center for Communications Research, 4320 Westerra Court, San Diego, California 92121, U.S.A.

Keywords

ENG
continued fractions, surds, automata

Bibliography

  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. 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).
  3. L. E. Baum and M. M. Sweet, Continued fractions of algebraic power series in characteristic 2, Ann. of Math. 103 (1976), 593-610.
  4. L. E. Baum and M. M. Sweet, Badly approximable power series in characteristic 2, Ann. of Math. 105 (1977), 573-580.
  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. D. G. Cantor, On the analogue of the division polynomials for hyperelliptic curves, J. Reine Angew. Math. 447 (1994), 91-145.
  7. M. Mendès France and A. J. van der Poorten, Some explicit continued fraction expansions, Mathematika 38 (1991), 1-9.
  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.
  9. W. H. Mills and D. P. Robbins, Continued fractions for certain algebraic power series, J. Number Theory 23 (1986), 388-404.
  10. J. Shallit, Real numbers with bounded partial quotients: A survey, Enseign. Math. 38 (1992), 151-187.
  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.
  12. A. J. van der Poorten and J. Shallit, Folded continued fractions, J. Number Theory 40 (1992), 237-250.
Acta Arithmetica
1994/68/4
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Pages:
295-305
Main language of publication
English
Received
1993-04-20
Accepted
1994-01-31
Published
1994
Exact and natural sciences