Optimal factorizations of rational numbers using factorization trees
Let $m_t(α)$ denote the $t$-metric Mahler measure of the algebraic number $α$. Recent work of the first author established that the infimum in $m_t(α)$ is attained by a single point $\barα= (α_1,\ldots,α_N)\in \overline{\mathbb Q}^N$ for all sufficiently large $t$. Nevertheless, no efficient method for locating $\bar α$ is known. In this article, we define a new tree data structure, called a factorization tree, which enables us to find $\barα$ when $α\in \mathbb Q$. We establish several basic properties of factorization trees, and use these properties to locate $\barα$ in previously unknown cases.
math.NT↗