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arXiv · 2104.02582

Minimal Mahler Measure in Cubic Number Fields

Lydia Eldredge·Kathleen Petersen
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Abstract

The minimal integral Mahler measure of a number field $K$, $M(\mathcal{O}_K)$, is the minimal Mahler measure of a non-torsion primitive element of $\mathcal{O}_K$. Upper and lower bounds, which depend on the discriminant, are known. We show that for cubics, the lower bounds are sharp with respect to its growth as a function of discriminant. We construct an algorithm to compute $M(\mathcal{O}_K)$ for all cubics with absolute value of the discriminant bounded by $N$.

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Lydia Eldredge, Kathleen Petersen. 2021-04-06. Minimal Mahler Measure in Cubic Number Fields. https://arxiv.org/abs/2104.02582

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