Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms

R. J. Stroeker; N. Tzanakis

Acta Arithmetica (1994)

  • Volume: 67, Issue: 2, page 177-196
  • ISSN: 0065-1036

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R. J. Stroeker, and N. Tzanakis. "Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms." Acta Arithmetica 67.2 (1994): 177-196. <http://eudml.org/doc/206625>.

@article{R1994,
author = {R. J. Stroeker, N. Tzanakis},
journal = {Acta Arithmetica},
keywords = {Mordell equation; cubic diophantine equation; integer points; Weierstraß equation; elliptic curve; linear form of elliptic logarithms},
language = {eng},
number = {2},
pages = {177-196},
title = {Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms},
url = {http://eudml.org/doc/206625},
volume = {67},
year = {1994},
}

TY - JOUR
AU - R. J. Stroeker
AU - N. Tzanakis
TI - Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms
JO - Acta Arithmetica
PY - 1994
VL - 67
IS - 2
SP - 177
EP - 196
LA - eng
KW - Mordell equation; cubic diophantine equation; integer points; Weierstraß equation; elliptic curve; linear form of elliptic logarithms
UR - http://eudml.org/doc/206625
ER -

References

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  6. [H] N. Hirata-Kohno, Formes linéaires de logarithmes de points algébriques sur les groupes algébriques, Invent. Math. 104 (1991), 401-433. Zbl0704.11016
  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. Zbl0488.12001
  9. [Lj] W. Ljunggren, A diophantine problem, J. London Math. Soc. (2) 3 (1971), 385-391. Zbl0215.34701
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  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. Zbl0656.14016
  14. [S3] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743. Zbl0729.14026
  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. Zbl0674.10012
  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. Zbl0657.10014
  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. Zbl0611.10008

Citations in EuDML Documents

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  1. Patrick Ingram, A quantitative primitive divisor result for points on elliptic curves
  2. Hui Lin Zhu, Jian Hua Chen, Integral Points on Certain Elliptic Curves
  3. R. J. Stroeker, On the sum of consecutive cubes being a perfect square
  4. J. R. Merriman, S. Siksek, N. P. Smart, Explicit 4-descents on an elliptic curve
  5. Benjamin M. M. de Weger, S -integral solutions to a Weierstrass equation
  6. J. Gebel, A. Pethő, H. G. Zimmer, Computing integral points on elliptic curves
  7. Roelof J. Stroeker, Benjamin M. M. de Weger, Solving elliptic diophantine equations: the general cubic case
  8. N. Tzanakis, Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms. The case of quartic equations
  9. Sinnou David, Minorations de formes linéaires de logarithmes elliptiques
  10. Éric Gaudron, Formes linéaires de logarithmes effectives sur les variétés abéliennes

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