Specialisation and reduction of continued fractions of formal power series

Ramanujan Journal

Volumn 9, Issue 1-2, 2005, Pages 83-91

  Van Der Poorten, Alfred J ^a  

^a Centre for Number Theory Research   (Australia)

Author keywords

Continued fraction expansion; Formal power series; Function field of characteristic zero

Indexed keywords

EID: 24344473436     PISSN: 13824090     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11139-005-0827-3     Document Type: Conference Paper

References (17)

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. R.M. Avanzi and U.M. Zannier, "Genus one curves defined by separated variable polynomials and a polynomial Pell equation," Acta Arith. 99(3) (2001), 227-256.
3. D.G. Cantor, "On the continued fractions of quadratic surds," Acta Arith. 68 (1994), 295-305.
4. E.W. Howe, F. Leprévost, and B. Poonen, "Large torsion subgroups of split Jacobians of curves of genus two or three," Forum Math. 12(3) (2000), 315-364.
5. D.S. Kubert, "Universal bounds on the torsion of elliptic curves," Proc. London Math. Soc. 33(3) (1976), 193-237.
6. M. Mendès France, A.J. van der Poorten, and J. Shallit, "On lacunary formal power series and their continued fraction expansion," in Number Theory in Progress (Proc. Conf. in honour of Andrzej Schinzel on the occasion of his 60th birthday) (K. Gyory, H. Iwaniec and J. Urbanowicz, eds,) Walter de Gruyter, Berlin, 1999, pp. 321-326.
7. H. Niederreiter and M. Vielhaber, "Linear complexity profiles: Hausdorff dimensions for almost perfect profiles and measures for general profiles," J. Complexity 13(3) (1997), 353-383.
8. H. Niederreiter and M. Vielhaber, "An algorithm for shifted continued fraction expansions in parallel linear time. Cryptography," Theoret. Comput. Sci. 226(1-2) (1999), 93-104.
9. A. Nitaj, "Détermination de courbes elliptiques pour la conjecture de Szpiro," Acta Arith. 85(4) (1998), 351-376;
10. "Isogenes des courbes elliptiques definies sur les rationnels", J. Comput. Math. 20(4) (2002), 337-348.
11. W.M. Schmidt, "On continued fractions and diophantine approximation in power series fields," Acta Arith. 95 (2000), 139-166.
12. A. van der Poorten, "Formal power series and their continued fraction expansion," in Algorithmic Number Theory, Proc. Third International Symposium, ANTS-III, (Joe Buhler ed.) Portland, Oregon, June 1998, Springer Lecture Notes in Computer Science 1423 (1998), 358-371.
13. A.J. van der Poorten, "Non-periodic continued fractions in hyperelliptic function fields' (Dedicated to George Szekeres on his 90th birthday), Bull. Austral. Math. Soc. 64 (2001), 331-343.
14. A.J. van der Poorten, "Periodic continued fractions and elliptic curves," High Primes and Misdemeanours: Lectures in honour of the 60th birthday of Hugh Cowie Williams (Alf van der Poorten and Andreas Stein, eds.), Fields Institute Communications 41, Amer. Math. Soc., 2004, 353-365.
15. See also "Elliptic curves and continued fractions," www.arxiv.org/math.NT/0403225.
16. A.J. van der Poorten and X.C. Tran, "Periodic continued fractions in elliptic function fields," in Algorithmic Number Theory, (Proc. Fifth International Symposium, ANTS-V, (Claus Fieker and David R. Kohel eds.) (Sydney, NSW, Australia July 2002), Springer Lecture Notes in Computer Science 2369 (2002), 390-404.
17. Jing Yu, "Arithmetic of hyperelliptic curves," manuscript marked Aspects of Mathematics, Hong Kong University, 1999; see pp. 4-6.