Counting rational points on smooth cubic curves
arXiv:1605.07856 · doi:10.1016/j.jnt.2017.12.001
Abstract
We use a global version of Heath-Brown's adic determinant method developed by Salberger to give upper bounds for the number of rational points of height at most on non-singular cubic curves defined over . The bounds are uniform in the sense that they only depend on the rank of the corresponding Jacobian.
arXiv comment10 pages. Comments are welcome