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Counting rational points on cubic curves
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Heath-Brown, Roger and Testa, Damiano (2010) Counting rational points on cubic curves. Science China Mathematics, Vol.53 (No.9). pp. 2259-2268. doi:10.1007/s11425-010-4037-0
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Official URL: http://dx.doi.org/10.1007/s11425-010-4037-0
Abstract
We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals. The bounds are uniform in the curve and involve the rank of the corresponding Jacobian. The method used in the proof is a combination of the “determinant method” with an m-descent on the curve.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Science China Mathematics | ||||
| Publisher: | Zhongguo Kexue Zazhishe | ||||
| ISSN: | 1674-7283 | ||||
| Official Date: | 2010 | ||||
| Dates: |
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| Volume: | Vol.53 | ||||
| Number: | No.9 | ||||
| Page Range: | pp. 2259-2268 | ||||
| DOI: | 10.1007/s11425-010-4037-0 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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