Pythagoras number of quartic orders containing $\sqrt{2}$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866911070795333632 |
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| author | He, Zilong Hu, Yong |
| author_facet | He, Zilong Hu, Yong |
| contents | Let $K$ be a quartic number field containing $\sqrt{2}$ and let $\mathcal{O}\subseteq K$ be an order such that $\sqrt{2}\in \mathcal{O}$. We prove that the Pythagoras number of $\mathcal{O}$ is at most 5. This confirms a conjecture of Krásenský, Raška and Sgallová. The proof makes use of Beli's theory of bases of norm generators for quadratic lattices over dyadic local fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_10468 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pythagoras number of quartic orders containing $\sqrt{2}$ He, Zilong Hu, Yong Number Theory 11E12, 11E25, 11E16 Let $K$ be a quartic number field containing $\sqrt{2}$ and let $\mathcal{O}\subseteq K$ be an order such that $\sqrt{2}\in \mathcal{O}$. We prove that the Pythagoras number of $\mathcal{O}$ is at most 5. This confirms a conjecture of Krásenský, Raška and Sgallová. The proof makes use of Beli's theory of bases of norm generators for quadratic lattices over dyadic local fields. |
| title | Pythagoras number of quartic orders containing $\sqrt{2}$ |
| topic | Number Theory 11E12, 11E25, 11E16 |
| url | https://arxiv.org/abs/2204.10468 |