Counting Rational Points on Cubic Curves
Number Theory
2009-09-24 v1
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.
Cite
@article{arxiv.0909.4246,
title = {Counting Rational Points on Cubic Curves},
author = {D. R. Heath-Brown and D. Testa},
journal= {arXiv preprint arXiv:0909.4246},
year = {2009}
}
Comments
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