Let $K\ne \mathbb{Q}$ be a number field, let $\alpha\in \mathcal{O}_K$ and let $f(X)\in \mathcal{O}_K[X]$. Denote the Mahler measure by $M$.
Is there any known result about the comparison of the values $M(\alpha)$ and $M(f(\alpha))$?
Let $K\ne \mathbb{Q}$ be a number field, let $\alpha\in \mathcal{O}_K$ and let $f(X)\in \mathcal{O}_K[X]$. Denote the Mahler measure by $M$.
Is there any known result about the comparison of the values $M(\alpha)$ and $M(f(\alpha))$?