English

Counting rational points on smooth cubic curves

Number Theory 2018-05-03 v2 Algebraic Geometry

Abstract

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

Keywords

Cite

@article{arxiv.1605.07856,
  title  = {Counting rational points on smooth cubic curves},
  author = {Manh Hung Tran},
  journal= {arXiv preprint arXiv:1605.07856},
  year   = {2018}
}

Comments

10 pages. Comments are welcome

R2 v1 2026-06-22T14:09:13.197Z