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arXiv · 2610.38831

Representations and $n$-universality of hermitian lattices over local and number fields

Yong Hu·Alexandre Lourdeaux
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Abstract

Let $E/F$ be a quadratic field extension. For any positive integer $n$ an integral hermitian form over $E/F$ is called $n$-universal if it represents all integral hermitian forms of rank $n$ over $E/F$. We study $n$-universal hermitian forms when $F$ is a local field of characteristic $\neq 2$ or a number field. In the local case, we characterize $n$-universal integral hermitian forms and provide finite criterion sets for $n$-universality. In the number field case, we show that an indefinite integral hermitian form is $n$-universal if and only if it is $n$-universal everywhere locally.

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Yong Hu, Alexandre Lourdeaux. 2026-10-28. Representations and $n$-universality of hermitian lattices over local and number fields. https://arxiv.org/abs/2610.38831

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