Inventiones mathematicae

, Volume 66, Issue 3, pp 395–404 | Cite as

Integer points and the rank of Thue elliptic curves

  • Joseph H. Silverman
Article

References

  1. 1.
    Baker, A.: A sharpening for the bounds for linear forms in logarithms II. Acta Arith.24, 33–36 (1973)Google Scholar
  2. 2.
    Davenport, H.: A note on Thue's theorem. Mathematika15, 76–87 (1968)Google Scholar
  3. 3.
    Davenport, H., Roth, K.F.: Rational approximations to algebraic numbers. Mathematika2, 1–20 (1955)Google Scholar
  4. 4.
    Dem'janenko, V.A.: Estimate of the remainder term in Tate's formula. Mat. Zam.3, 271–278 (1968)Google Scholar
  5. 5.
    Dem'janenko, V.A.: On Tate height and the representation of a number by binary forms. Math. USSR Isv.8, 463–476 (1974)Google Scholar
  6. 6.
    Fel'dman, N.I.: An effective refinement of the exponent in Liouville's theorem. Math. USSR Isv.5, 985–1002 (1971)Google Scholar
  7. 7.
    Gelfond, A.O.: Transcendental and algebraic numbers, translated by L. Boron, Dover, N.Y., 1960Google Scholar
  8. 8.
    Hall, M.: The diophantine equationx 3 −y 2=k in: Atkin, A., Birch, B., eds. Computers in number theory, London: Academic Press 1971Google Scholar
  9. 9.
    Hooley, C.: On binary cubic forms. J. Reine Ang. Math.226, 30–87 (1967)Google Scholar
  10. 10.
    Hooley, C.: On the numbers representable as the sum of two cubes. J. Reine Ang. Math.314, 146–173 (1980)Google Scholar
  11. 11.
    Lang, S.: Elliptic curves: Diophantine analysis. Grundlehren der Math. Wissenschaften Vol. 231, Berlin: Springer 1978Google Scholar
  12. 12.
    Lewis, D.J., Mahler, K.: On the representation of integers by binary forms. Acta Arith.6, 333–363 (1961)Google Scholar
  13. 13.
    Mahler, K.: On the lattice points on curves of genus 1. Proc. London Math. Soc. Second Series39, 431–466 (1935)Google Scholar
  14. 14.
    Manin, J., Zahrin, J.: Height on families of abelian varieties. Math. USSR Sbor.18, 169–179 (1972)Google Scholar
  15. 15.
    Mazur, B.: Modular curves and the Eisenstein ideal. IHES Publ. Math.47, 33–186 (1977)Google Scholar
  16. 16.
    Salmon, G.: Lessons introductory to the modern higher algebra, 3rd ed., Cambridge: Hodges, Foster, and Co. 1876Google Scholar
  17. 17.
    Schinzel, A.: Review of “Über die Gleichungax n −by n=z und das Catalansche Problem” by S. Hyyrö, Zentralblatt für Math.137, 257–258 (1967)Google Scholar
  18. 18.
    Silverman, J.: Lower bound for the canonical height on elliptic curves. Duke Math. J.48, 633–648 (1981)Google Scholar
  19. 19.
    Silverman, J.: The Néron-Tate height on elliptic curves. Ph.D. Thesis, Harvard University, 1981Google Scholar
  20. 20.
    Thue, A.: Über Annäherungswerte Algebraischer Zahlen. J. Reine Angew. Math.135, 284–305 (1909)Google Scholar
  21. 21.
    Zimmer, H.: On the difference of the Weil height and the Néron-Tate height. Math. Zeit.147, 35–51 (1976)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Joseph H. Silverman
    • 1
  1. 1.Mathematics DepartmentHarvard UniversityCambridgeUSA

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