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The canonical height and integral points on elliptic curves

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References

  1. Apostol, T.: Introduction to analytic number theory. Berlin-Heidelberg-New York: Springer 1976

    Google Scholar 

  2. Apostol, T.: Modular functions and Dirichlet series in number theory. Berlin-Heidelberg-New York: Springer 1976

    Google Scholar 

  3. Blanksby, P.E., Montgomery, H.L.: Algebraic integers near the unit circle. Acta Arith.18, 355–369 (1971)

    Google Scholar 

  4. Cox, D., Zucker, S.: Intersection numbers of sections of elliptic surfaces. Invent. Math.53, 1–44 (1979)

    Google Scholar 

  5. Dem'janenko, V.A.: Estimate of the remainder term in Tate's formula. Mat. Zametki.3, 271–278 (1968)

    Google Scholar 

  6. Dem'janenko, V.A.: On Tate height and the representation of numbers by binary forms. Math. USSR, Izv.8, 463–476 (1974)

    Google Scholar 

  7. Frey, G.: Links between stable elliptic curves and certain Diophantine equations. Ann. Univ. Sar., Ser. Math.1, 1–40 (1986)

    Google Scholar 

  8. Frey, G.: Letter to Serge Lang. Sept. 3, 1986

  9. Lang, S.: Elliptic curves: Diophantine analysis. (Grundlehren der Math. Wissenschaften, Vol. 231). Berlin-Heidelberg-New York: Springer 1978

    Google Scholar 

  10. Mason, R.C.: The hyperelliptic equation over function fields. Math. Proc. Camb. Philos. Soc.93, 219–230 (1983)

    Google Scholar 

  11. Ogg, A.: Elliptic curves and wild ramification. Am. J. Math.89, 1–21 (1967)

    Google Scholar 

  12. Rosser, J.B., Schoenfeld, L.: Sharper bounds for the Chebyshev functions θ(x) and ψ(x). Math. Comput.29, 243–269 (1975)

    Google Scholar 

  13. Schmidt, W.: Thue's equation over function fields. Aust. Math. Soc. Gaz.25, 385–422 (1978)

    Google Scholar 

  14. Serre, J.-P.: A course in arithmetic. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  15. Serre, J.-P., Tate, J.: Good reduction of abelian varieties. Ann. Math.68, 492–517 (1968)

    Google Scholar 

  16. Shimura, G.: Introduction to the arithmetic theory of automorphic forms. Princeton N.J.: Princeton University Press 1971

    Google Scholar 

  17. Siegel, C.L.: Über Gitterpunkte in convexen Körpern und ein damit zusammenhängendes Extremalproblem. Acta Math.65, 307–323 (1935)

    Google Scholar 

  18. Silverman, J.H.: Lower bound for the canonical height on elliptic curves. Duke Math. J.48, 633–648 (1981)

    Google Scholar 

  19. Silverman, J.H.: Integer points and the rank of Thue elliptic curves. Invent. Math.66, 395–404 (1982)

    Google Scholar 

  20. Silverman, J.H.: TheS-unit equation over function fields. Math. Proc. Camb. Philos. Soc.95, 3–4 (1984)

    Google Scholar 

  21. Silverman, J.H.: The arithmetic of elliptic curves. Berlin-Heidelberg-New York: Springer 1986

    Google Scholar 

  22. Silverman, J.H.: Heights and elliptic curves, In: (Cornell, G., Silverman, J., (eds.) Arithmetic geometry). Berlin-Heidelberg-New York: Springer 1986

    Google Scholar 

  23. Silverman, J.H.: A quantitative version of Siegel's theorem. J. Reine Angew. Math.378, 60–100 (1987)

    Google Scholar 

  24. Silverman, J.H.: Computing heights on elliptic curves. Math. Comput., to appear

  25. Szpiro, L.: Séminaire sur les pinceaux de courbes de genre au moins deux. Astérisque86, 44–78 (1981)

    Google Scholar 

  26. Tate, J.: Modular functions of one variable IV. (Lecture Notes in Math., Vol. 476, Birch, B., Kuyk, W. (eds.)). Berlin-Heidelberg-New York: Springer 1975

    Google Scholar 

  27. Vojta, P.: Diophantine approximations and value distribution theory. (Lecture Notes in Math., Vol. 1239). Berlin-Heidelberg-New York: Springer 1987

    Google Scholar 

  28. Zimmer, H.: On the difference of the Weil height and the Néron-Tate height. Math. Z.147, 35–51 (1976)

    Google Scholar 

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Research supported by NSF grant DMS 8612393 and a Sloan Foundation Fellowship

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Hindry, M., Silverman, J.H. The canonical height and integral points on elliptic curves. Invent Math 93, 419–450 (1988). https://doi.org/10.1007/BF01394340

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