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arXiv · 2204.10468

Pythagoras number of quartic orders containing $\sqrt{2}$

Zilong He·Yong Hu
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Abstract

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 Kr\'{a}sensk\'{y}, Ra\v{s}ka and Sgallov\'a. The proof makes use of Beli's theory of bases of norm generators for quadratic lattices over dyadic local fields.

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Zilong He, Yong Hu. 2022-04-22. Pythagoras number of quartic orders containing $\sqrt{2}$. https://doi.org/10.16205/j.cnki.cama.2024.0020

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