Sieving for rational points on hyperelliptic curves
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- by Samir Siksek PDF
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Abstract:
We give a new and efficient method of sieving for rational points on hyperelliptic curves. This method is often successful in proving that a given hyperelliptic curve, suspected to have no rational points, does in fact have no rational points; we have often found this to be the case even when our curve has points over all localizations $\mathbb {Q}_p$. We illustrate the practicality of the method with some examples of hyperelliptic curves of genus $1$.References
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Additional Information
- Samir Siksek
- Affiliation: Institute of Mathematics and Statistics, Cornwallis Building, University of Kent, Canterbury, UK
- Address at time of publication: Department of Mathematics, College of Science, PO Box 36, Sultan Qaboos University, Oman
- Email: siksek@squ.edu.om
- Received by editor(s): November 21, 1996
- Received by editor(s) in revised form: January 28, 1997, and November 29, 1999
- Published electronically: March 7, 2001
- Additional Notes: The author’s research was conducted while the author was at the University of Kent and funded by a grant from the EPSRC (UK).
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 70 (2001), 1661-1674
- MSC (2000): Primary 11G05; Secondary 11Y16, 11Y50
- DOI: https://doi.org/10.1090/S0025-5718-01-01275-3
- MathSciNet review: 1836925
Dedicated: To Shaheen