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arXiv · 2407.10343

On trace-one generators of abelian cubic fields

Andrew O'Desky
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Abstract

Let $K$ be a tamely ramified abelian cubic number field with discriminant $D_K$. We prove that the number of trace-one monic integral polynomials with root field $K$ and height $H$ is equal to the number of ideals in the quadratic field $\mathbb Q(\sqrt{-3})$ with norm $H^2 D_K^{-1/2}$.

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Andrew O'Desky. 2024-07-14. On trace-one generators of abelian cubic fields. https://arxiv.org/abs/2407.10343

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