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arXiv · 0909.4246

Counting Rational Points on Cubic Curves

D. R. Heath-Brown·D. Testa
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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.

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BibTeXRIS

D. R. Heath-Brown, D. Testa. 2009-09-23. Counting Rational Points on Cubic Curves. https://arxiv.org/abs/0909.4246

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