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Sieving for rational points on hyperelliptic curves
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Siksek, Samir (2001) Sieving for rational points on hyperelliptic curves. Mathematics of Computation, Vol.70 (No.236). pp. 1661-1674. doi:10.1090/S0025-5718-01-01275-3 ISSN 0025-5718.
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Official URL: http://dx.doi.org/10.1090/S0025-5718-01-01275-3
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 Qp. We illustrate the practicality of the
method with some examples of hyperelliptic curves of genus 1.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Sieves (Mathematics), Elliptic functions, Rational points (Geometry) | ||||
Journal or Publication Title: | Mathematics of Computation | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0025-5718 | ||||
Official Date: | 2001 | ||||
Dates: |
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Volume: | Vol.70 | ||||
Number: | No.236 | ||||
Page Range: | pp. 1661-1674 | ||||
DOI: | 10.1090/S0025-5718-01-01275-3 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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