ArticleOriginal scientific text

Title

Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms

Authors 1, 2

Affiliations

  1. Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands
  2. Department of Mathematics, University of Crete, P.O. Box 470, 714 09 Iraklion, Greece

Bibliography

  1. [AS] M. Abramowitz and I. Stegun (eds.), Handbook of Mathematical Functions, Dover, New York, 1964.
  2. [BM] J.-B. Bost et J.-F. Mestre, Moyenne arithmético-géométrique et périodes des courbes de genre 1 et 2, Gazette de Mathématiciens, S.M.F., Octobre 1988.
  3. [Br] A. Bremner, An equation of Mordell, Math. Comp. 29 (1975), 925-928.
  4. [C] D. A. Cox, The arithmetic-geometric mean of Gauss, Enseign. Math. 30 (1984), 275-330.
  5. [D] S. David, Minorations de formes linéaires de logarithmes elliptiques, Publ. Math. Univ. Pierre et Marie Curie 106, Problèmes diophantiens 1991-1992, exposé no. 3.
  6. [H] N. Hirata-Kohno, Formes linéaires de logarithmes de points algébriques sur les groupes algébriques, Invent. Math. 104 (1991), 401-433.
  7. [La] S. Lang, Elliptic Curves; Diophantine Analysis, Grundlehren Math. Wiss. 231, Springer, Berlin, 1978.
  8. [LLL] A. K. Lenstra, H. W. Lenstra Jr., and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534.
  9. [Lj] W. Ljunggren, A diophantine problem, J. London Math. Soc. (2) 3 (1971), 385-391.
  10. [Ma] D. W. Masser, Elliptic Functions and Transcendence, Lecture Notes in Math. 437, Springer, Berlin, 1975.
  11. [Mo] L. J. Mordell, Diophantine Equations, Pure Appl. Math. 30, Academic Press, London and New York, 1969.
  12. [S1] J. H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Math. 106, Springer, New York, 1986.
  13. [S2] J. H. Silverman, Computing heights on elliptic curves, Math. Comp. 51 (1988), 339-358.
  14. [S3] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743.
  15. [STo] R. J. Stroeker and J. Top, On the equation Y² = (X+p)(X²+p²), Rocky Mountain J. Math. 24 (2) (1994), to appear.
  16. [STz] R. J. Stroeker and N. Tzanakis, On the application of Skolem's p-adic method to the solution of Thue equations, J. Number Theory 29 (2) (1988), 166-195.
  17. [TdW] N. Tzanakis and B. M. M. de Weger, On the practical solution of the Thue equation, J. Number Theory 31 (2) (1989), 99-132.
  18. [dW] B. M. M. de Weger, Algorithms for Diophantine Equations, CWI Tract 65, Stichting Mathematisch Centrum, Amsterdam, 1989.
  19. [WW] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge University Press, New York, 1978.
  20. [Wu] G. Wüstholz, Recent progress in transcendence theory, in: Number Theory, Noordwijkerhout 1983, Lecture Notes in Math. 1068, Springer, Berlin, 1984, 280-296.
  21. [Z] D. Zagier, Large integral points on elliptic curves, Math. Comp. 48 (1987), 425-436.
Pages:
177-196
Main language of publication
English
Received
1993-11-02
Published
1994
Exact and natural sciences