LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Siksek, Samir (2001)
Publisher: American Mathematical Society
Languages: English
Types: Article
Subjects: QA

Classified by OpenAIRE into

arxiv: Mathematics::Algebraic Geometry, Mathematics::Number Theory, Nonlinear Sciences::Exactly Solvable and Integrable Systems
We give a new and efficient method of sieving for rational points\ud on hyperelliptic curves. This method is often successful in proving that a\ud given hyperelliptic curve, suspected to have no rational points, does in fact\ud have no rational points; we have often found this to be the case even when our\ud curve has points over all localizations Qp. We illustrate the practicality of the\ud method with some examples of hyperelliptic curves of genus 1.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [AHU] A. V. Aho, J. E. Hopcroft, J. D. Ullman, Data Structures and Algorithms, AddisonWesley, 1982. MR 84f:68001
    • [Cal] J. W. S. Cassels, Local Fields, LMS Student Texts, Cambridge University Press, 1986. MR 87i:11172
    • [Ca2] J. W. S. Cassels, Survey Article: Diophantine Equations with Special Reference to Elliptic Curves, J.L.M.S. 41 (1966), 193-291. MR 33:7299
    • [Ca3] J. W. S. Cassels, Second Descents for Elliptic Curves, J. reine angew. Math. 494 (1998), 101{127. MR 99d:11058
    • [Cohen] H. Cohen, A Course in Computational Algebraic Number Theory, GTM 138, SpringerVerlag, third corrected printing, 1996. MR 94i:11105
    • [Cohn] P. M. Cohn, Algebra, Volume I, second edition, John Wiley and Sons, 1982. MR 83e:00002
    • [Cre1] J. E. Cremona, Algorithms for Modular Elliptic Curves, second edition, Cambridge University Press, 1997. MR 99e:11068
    • [Cre2] J. E. Cremona, Personal Communication, 1996.
    • [Me,Si,Sm] J.R. Merriman, S. Siksek and N.P. Smart, Explicit 4-Descents on an Elliptic Curve, Acta Arith. LXXVII (1996), 385-404. MR 97j:11027
    • [Sil] J. H. Silverman, The Arithmetic of Elliptic Curves, GTM 106, Springer-Verlag, 1986. MR 87g:11070 Institute of Mathematics and Statistics, Cornwallis Building, University of Kent,
    • Canterbury, UK Current address: Department of Mathematics, College of Science, PO Box 36, Sultan Qaboos
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article