Effective results on linear dependence for elliptic curves

Min Sha; Igor E. Shparlinski

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arXiv · 1410.1596

Effective results on linear dependence for elliptic curves

Min Sha·Igor E. Shparlinski

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Abstract

Given a subgroup $\Gamma$ of rational points on an elliptic curve $E$ defined over ${\mathbf Q}$ of rank $r \ge 1$ and any sufficiently large $x \ge 2$, assuming that the rank of $\Gamma$ is less than $r$, we give upper and lower bounds on the canonical height of a rational point $Q$ which is not in the group $\Gamma$ but belongs to the reduction of $\Gamma$ modulo every prime $p \le x$ of good reduction for $E$.

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Min Sha, Igor E. Shparlinski. 2014-10-07. Effective results on linear dependence for elliptic curves. https://arxiv.org/abs/1410.1596

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