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arXiv · 1408.4162

Optimal factorizations of rational numbers using factorization trees

Charles L. Samuels·Tanner J. Strunk
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Abstract

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.

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Charles L. Samuels, Tanner J. Strunk. 2014-08-18. Optimal factorizations of rational numbers using factorization trees. https://doi.org/10.1142/s1793042115500402

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