Counting rational points on cubic curves

DOI10.1007/s11425-010-4037-0zbMath1229.11052arXiv0909.4246OpenAlexW2042773224MaRDI QIDQ625847

Damiano Testa, D. R. Heath-Brown

Publication date: 25 February 2011

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.4246

zbMATH Keywords

elliptic curvesrational pointscounting functioncubic curvesdeterminant method\(m\)-descent

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Counting solutions of Diophantine equations (11D45) Cubic and quartic Diophantine equations (11D25)

Related Items (2)

Uniform bounds for rational points on complete intersections of two quadric surfaces ⋮ Counting rational points on smooth cubic curves

Cites Work

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• Modular curves and the Eisenstein ideal
• Points of small height on elliptic curves
• The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène).
• The number of integral points on arcs and ovals
• Indefinite Quadratic Forms in Many Variables (II)
• Vanishing theorems.
• On a Differential-Geometric Method in the Theory of Analytic Stacks

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