# On the continued fractions of quadratic surds

Acta Arithmetica (1994)

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

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topDavid 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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- [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] 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] L. E. Baum and M. M. Sweet, Badly approximable power series in characteristic 2, Ann. of Math. 105 (1977), 573-580. Zbl0352.10017
- [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. Zbl0788.14026
- [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. Zbl0626.10029
- [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] J. Shallit, Real numbers with bounded partial quotients: A survey, Enseign. Math. 38 (1992), 151-187. Zbl0753.11006
- [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] A. J. van der Poorten and J. Shallit, Folded continued fractions, J. Number Theory 40 (1992), 237-250. Zbl0753.11005

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