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arXiv · 2101.11384

On the Pythagoras number of the simplest cubic fields

Magdaléna Tinková
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Abstract

The simplest cubic fields $\mathbb{Q}(\rho)$ are generated by a root $\rho$ of the polynomial $x^3-ax^2-(a+3)x-1$ where $a\geq -1$. In this paper, we will show that the Pythagoras number of the order $\mathbb{Z}[\rho]$ is equal to $6$ for $a\geq 3$.

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Magdaléna Tinková. 2021-01-27. On the Pythagoras number of the simplest cubic fields. https://doi.org/10.4064/aa221003-27-6

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