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arXiv · 2307.07118

Lifting problem for universal quadratic forms over totally real cubic number fields

Daejun Kim·Seok Hyeong Lee
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Abstract

Lifting problem for universal quadratic forms asks for totally real number fields $K$ that admit a positive definite quadratic form with coefficients in $\mathbb{Z}$ that is universal over the ring of integers of $K$. In this paper, we show that $K=\mathbb{Q}(\zeta_7+\zeta_7^{-1})$ is the only such totally real cubic field. Moreover, we show that there is no such biquadratic field.

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Daejun Kim, Seok Hyeong Lee. 2023-07-14. Lifting problem for universal quadratic forms over totally real cubic number fields. https://doi.org/10.1112/blms.12988

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