Quasi-elliptic integrals and periodic continued fractions

Monatshefte fur Mathematik

Volumn 131, Issue 2, 2000, Pages 155-169

  Van Der Poorten, Alfred J ^a   Tran, Xuan Chuong ^a  

^a MACQUARIE UNIVERSITY   (Australia)

Author keywords

Function field; Periodic continued fraction

Indexed keywords

EID: 0007265213     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s006050070018     Document Type: Article

References (29)

1. Abel NH (1826) Über die Integration der Differential-Formel ρdx/√R, wenn R und ρ ganze Funktionen sind. J für Math 1: 185-221
2. Adams WW, Razar MJ (1980) Multiples of points on elliptic curves and continued fractions. Proc London Math Soc 41: 481-498
3. Berry TG (1990) On periodicity of continued fractions in hyperelliptic function fields. Arch Math 55: 259-266
4. Bombieri E, Cohen PB (1998) Siegel's lemma, Padé approximations and Jacobians (with an appendix by Umberto Zannier, and dedicated to Ennio De Giorgi). Ann Scuola Norm Sup Pisa Cl Sci (4) 25: 155-178
5. Cantor DG (1994) On the continued fractions of quadratic surds. Acta Arith 68: 295-305
6. Cassels JWS, Flynn EV (1996) Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2. London Math Soc Lect Notes 230. Cambridge: Univ Press
7. 2+γx+δ. ibid 9: 225-246
8. 2+γx+δ. ibid 9: 225-246
9. Davenport JH (1981) On the integration of algebraic functions. Lect Notes Computer Sci 102. Berlin Heidelberg New York: Springer
10. Dubois et E, Paysant-Le Roux R (1991) Sur la longeur du developpement en fraction continue de √f(n). Astérisque 198-200: 107-119
11. Friesen C, Continued fraction characterization and generic ideals. In [11], pp 465-474
12. Goss D, Hayes DR, Rosen MI (eds.) (1991) The Arithmetic of Function Fields. Proc workshop held at the Ohio State Univ, Columbus, Ohio, June 17-26, Ohio State Univ Math Res Inst Publ 2. Berlin: de Gruyter
13. Howe EW, Leprévost F, Poonen B (2000) Large torsion subgroups of split Jacobians of curves of genus two or three. Forum Math 12: 315-364
14. Kaplansky I (1957) An Introduction to Differential Algebra. Publ Inst Math Univ Nancago, V. Paris: Hermann
15. Knuth DE (1969) The Art of Computer Programming, vol 2: Seminumerical Algorithms
16. Leprévost F (1993) Points rationnels de torsion de jacobiennes de certaines courbes de genre 2. CR Acad Sci Paris Ser I Math 316: 819-821
17. Mazur B (1977) Modular curves and the Eisenstein ideal. Inst Hautes Études Sci Publ Math 47: 33-186
18. 2 = -3. J Théorie de Nombres de Bordeaux 6: 421-459
19. van der Poorten AJ (1986) An introduction to continued fractions. In: Loxton JH, van der Poorten AJ (eds) Diophantine Analysis, pp 99-138. Cambridge: Univ Press
20. van der Poorten A (1998) Formal power series and their continued fraction expansion. In: Buhler J (ed) Algorithmic Number Theory Lect Notes Computer Sci 1423. Berlin Heidelberg New York: Springer
21. van der Poorten AJ, Williams HC (1999) On certain continued fraction expansions of fixed period length. Acta Arith 89: 23-35
22. van der Poorten A (1999) Reduction of continued fractions of formal power series. In: Berndt B, Gesztesy F (eds) Continued Fractions: From Analytic Number Theory to Constructive Approximation (Columbia, Missouri May, 1998), Contemporary Math 236: 343-355
23. Rosenlicht M (1972) Integration in finite terms. Amer Math Monthly 79: 963-972; Liouville's theorem on functions with elementary integrals. Pacific J Math 24: 153-161 (1968); On Liouville's Theory of elementary functions. ibid 65: 485-492 (1976)
24. Rosenlicht M (1972) Integration in finite terms. Amer Math Monthly 79: 963-972; Liouville's theorem on functions with elementary integrals. Pacific J Math 24: 153-161 (1968); On Liouville's Theory of elementary functions. ibid 65: 485-492 (1976)
25. Rosenlicht M (1972) Integration in finite terms. Amer Math Monthly 79: 963-972; Liouville's theorem on functions with elementary integrals. Pacific J Math 24: 153-161 (1968); On Liouville's Theory of elementary functions. ibid 65: 485-492 (1976)
26. Schinzel A (1961) On some problems of the arithmetical theory of continued fractions. Acta Arith 6: 393-413; ibid 7: 287-298 (1962)
27. Schinzel A (1961) On some problems of the arithmetical theory of continued fractions. Acta Arith 6: 393-413; ibid 7: 287-298 (1962)
28. Schmidt WM (1999) On continued fractions and diophantine approximation in power series fields (Manuscript)
29. Tran XC, PhD Thesis, Macquarie University, Sydney (in preparation)