Number Theory Seminar

Speaker: Linda Frey (Basel)

Title: Explicit Small Height Bound for $\mathbb{Q} (E_\text{tor})$.

Abstract: Let $E$ be an elliptic curve defined over $\mathbb{Q}$. We will show that there exists an explicit constant $C>0$ which is only dependent on the conductor and the $j-$invariant of $E$ such that the absolute logarithmic Weil height of an $\alpha \in \mathbb{Q} (E_\text{tor})^*\setminus \mu_\infty$ is always greater than $C$ where $E_\text{tor}$ denotes all the torsion points of $E$ and $\mu_\infty$ are the roots of unity.