Skip to main content
Log in

Representations of integers by binary forms and the rank of the Mordell-Weil group

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

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

    Google Scholar 

  2. Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: John Wiley and Sons 1978

    Google Scholar 

  3. Honda, T.: Isogenies, rational points, and section points of group varieties. Jap. J. Math.30, 84–101 (1960)

    Google Scholar 

  4. Lang, S.: Fundamentals of Diophantine geometry. Berlin-Heidelberg-New York: Springer 1983

    Google Scholar 

  5. Lang, S.: Algebraic number theory. Reading, MA: Addison-Wesley 1970

    Google Scholar 

  6. Lang, S.: Elliptic curves: Diophantine analysis. Grund. Math. Wiss. 231. Berlin-Heidelberg-New York: Springer 1978

    Google Scholar 

  7. Lewis, D.J., Mahler, K.: On the representations of integers by binary forms. Acta Arith.6, 333–363 (1961)

    Google Scholar 

  8. Mignotte, M.: Quelques remarques sur l'approximation rationelle des nombres algébriques. J. Reine Angew. Math.268/269, 341–347 (1974)

    Google Scholar 

  9. Mumford, D.: Abelian varieties. Tata Institute, Bombay: Oxford University Press 1974

    Google Scholar 

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

    Google Scholar 

  11. Silverman, J.: Lower bounds for height functions. (to appear)

  12. Thue, A.: Über Annäherungswerte algebraischer Zahlen. J. Reine Angew. Math.135, 384–305 (1909)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Silverman, J.H. Representations of integers by binary forms and the rank of the Mordell-Weil group. Invent Math 74, 281–292 (1983). https://doi.org/10.1007/BF01394317

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01394317

Keywords

Navigation