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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 ≠ 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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Cite

BibTeXRIS
BibTeX
@misc{hu2026representations,
  title = {{Representations and $n$-universality of hermitian lattices over local and number fields}},
  author = {Yong Hu and Alexandre Lourdeaux},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38831},
  eprint = {2610.38831},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38831},
}
RIS
TY  - UNPB
TI  - Representations and n-universality of hermitian lattices over local and number fields
AU  - Yong Hu
AU  - Alexandre Lourdeaux
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38831
UR  - https://arxiv.org/abs/2610.38831
AB  - 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 ≠ 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.
ER  -