On the continued fractions of quadratic surds

• Autorzy: David G. Cantor
• Języki publikacji: EN

Słowa kluczowe

EN

continued fractions; surds; automata

Kategorie tematyczne

• 14H45: Special curves and curves of low genus
• 14H40: Jacobians, Prym varieties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1994
• Tom: 68
• Numer: 4
• Strony: 295-305

Daty

wydano

1994

otrzymano

1993-04-20

poprawiono

1994-01-31

Twórcy

autor

David G. Cantor

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

Bibliografia

• [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.