ArticleOriginal scientific text
Title
Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms
Authors 1, 2
Affiliations
- Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands
- Department of Mathematics, University of Crete, P.O. Box 470, 714 09 Iraklion, Greece
Bibliography
- [AS] M. Abramowitz and I. Stegun (eds.), Handbook of Mathematical Functions, Dover, New York, 1964.
- [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.
- [Br] A. Bremner, An equation of Mordell, Math. Comp. 29 (1975), 925-928.
- [C] D. A. Cox, The arithmetic-geometric mean of Gauss, Enseign. Math. 30 (1984), 275-330.
- [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.
- [H] N. Hirata-Kohno, Formes linéaires de logarithmes de points algébriques sur les groupes algébriques, Invent. Math. 104 (1991), 401-433.
- [La] S. Lang, Elliptic Curves; Diophantine Analysis, Grundlehren Math. Wiss. 231, Springer, Berlin, 1978.
- [LLL] A. K. Lenstra, H. W. Lenstra Jr., and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534.
- [Lj] W. Ljunggren, A diophantine problem, J. London Math. Soc. (2) 3 (1971), 385-391.
- [Ma] D. W. Masser, Elliptic Functions and Transcendence, Lecture Notes in Math. 437, Springer, Berlin, 1975.
- [Mo] L. J. Mordell, Diophantine Equations, Pure Appl. Math. 30, Academic Press, London and New York, 1969.
- [S1] J. H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Math. 106, Springer, New York, 1986.
- [S2] J. H. Silverman, Computing heights on elliptic curves, Math. Comp. 51 (1988), 339-358.
- [S3] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743.
- [STo] R. J. Stroeker and J. Top, On the equation Y² = (X+p)(X²+p²), Rocky Mountain J. Math. 24 (2) (1994), to appear.
- [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.
- [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.
- [dW] B. M. M. de Weger, Algorithms for Diophantine Equations, CWI Tract 65, Stichting Mathematisch Centrum, Amsterdam, 1989.
- [WW] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge University Press, New York, 1978.
- [Wu] G. Wüstholz, Recent progress in transcendence theory, in: Number Theory, Noordwijkerhout 1983, Lecture Notes in Math. 1068, Springer, Berlin, 1984, 280-296.
- [Z] D. Zagier, Large integral points on elliptic curves, Math. Comp. 48 (1987), 425-436.