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arXiv · 2003.13188

Lagrange spectrum of a circle over the Eisensteinian field

Byungchul Cha·Heather Chapman·Brittany Gelb·Chooka Weiss
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Abstract

We study an intrinsic Lagrange spectrum of the unit circle $|z|=1$ in the complex plane with respect to the Eisensteinian field $\mathbb{Q}(\sqrt{-3})$. We prove that the minimum of the Lagrange spectrum is $2$ and that its smallest accumulation point is $4/\sqrt{3}$. In addition, we characterize the set of all values in the spectrum between $2$ and $4/\sqrt3$.

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Byungchul Cha, Heather Chapman, Brittany Gelb, Chooka Weiss. 2020-03-30. Lagrange spectrum of a circle over the Eisensteinian field. https://arxiv.org/abs/2003.13188

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