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arXiv · 1805.05450

The Lind-Lehmer Constant for $\mathbb Z_2^r \times \mathbb Z_{4}^s$

Michael J. Mossinghoff·Vincent Pigno·Christopher Pinner
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Abstract

We show that the minimal positive logarithmic Lind-Mahler measure for a group of the form $G=\mathbb Z_2^r\times\mathbb Z_4^s$ with $|G|\geq 4$ is $\frac{1}{|G|} \log (|G|-1).$ We also show that for $G=\mathbb Z_2 \times \mathbb Z_{2^n}$ with $n\geq 3$ this value is $\frac{1}{|G|} \log 9.$ Previously the minimal measure was only known for $2$-groups of the form $\mathbb Z_2^k$ or $\mathbb Z_{2^k}.$

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Michael J. Mossinghoff, Vincent Pigno, Christopher Pinner. 2018-05-14. The Lind-Lehmer Constant for $\mathbb Z_2^r \times \mathbb Z_{4}^s$. https://doi.org/10.2140/moscow.2019.8.151

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