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On trace-one generators of abelian cubic fields (2407.10343v1)
Published 14 Jul 2024 in math.NT
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 $H2 D_K{-1/2}$.
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