Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    DRAZIOTIS, KONSTANTINOS A. 2011. ON THE NUMBER OF INTEGER POINTS ON THE ELLIPTIC CURVE y2= x3+ Ax. International Journal of Number Theory, Vol. 07, Issue. 03, p. 611.


    Surroca, Andrea 2007. Sur l'effectivité du théorème de Siegel et la conjecture abc. Journal of Number Theory, Vol. 124, Issue. 2, p. 267.


    ×
  • Bulletin of the Australian Mathematical Society, Volume 57, Issue 2
  • April 1998, pp. 199-206

On the size of integer solutions of elliptic equations

  • Yann Bugeaud (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972700031592
  • Published online: 01 April 2009
Abstract

We improve upon earlier effective bounds for the magnitude of integer points on an elliptic curve ε defined over a number field K. We slightly refine the dependence on the discriminant of K. In most of the previous papers, the estimates obtained are exponential in the height of ε. In this work, taking also into consideration the prime ideals dividing the discriminant of ε, we provide a totally explicit bound which is only polynomial in the height.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      On the size of integer solutions of elliptic equations
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      On the size of integer solutions of elliptic equations
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      On the size of integer solutions of elliptic equations
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[6]S. Lang , Elliptic curves: Diophantine analysis (Springer-Verlag, Berlin, Heidelberg, New York, 1978).

[12]J.H. Silverman , The arithmetic of elliptic curves, Graduate Texts in Math. 106 (Springer-Verlag, Berlin, Heidelberg, New York, 1986).

[13]V.G. Sprindžuk , Classical Diophantine equations, Lecture Notes in Math. 1559 (Springer-Verlag, Berlin, Heidelberg, New York, 1993).

[14]P.M. Voutier , ‘An upper bound for the size of integer solutions to Ym = f(X)’, J. Number Theory 53 (1995), 247271.

[15]M. Waldschmidt , ‘Minorations de combinaisons linéaires de logarithmes de nombres algébriques’, Canad. J. Math. 45 (1993), 176224.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax