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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

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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:
DateEvent
2010Published
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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