Counting rational points on smooth cubic curves

Manh Hung Tran

doi:10.1016/j.jnt.2017.12.001

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arXiv · 1605.07856

Counting rational points on smooth cubic curves

Manh Hung Tran

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Abstract

We use a global version of Heath-Brown's $p-$adic determinant method developed by Salberger to give upper bounds for the number of rational points of height at most $B$ on non-singular cubic curves defined over $\mathbb{Q}$. The bounds are uniform in the sense that they only depend on the rank of the corresponding Jacobian.

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BibTeX RIS

Manh Hung Tran. 2017-02-10. Counting rational points on smooth cubic curves. https://doi.org/10.1016/j.jnt.2017.12.001

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