The greatest common valuation of ${\varphi }_n$ and ${\psi }_n^2$ at points on elliptic curves

Paul Voutier, Minoru Yabuta

Given a minimal model of an elliptic curve, $E/K$, over a finite extension, $K$, of ${\mathbb{Q}}_p$ for any rational prime, $p$, and any point $P\in E(K)$ of infinite order, we…