论文标题
pythagoras数量的四分之一订单包含$ \ sqrt {2} $
Pythagoras number of quartic orders containing $\sqrt{2}$
论文作者
论文摘要
令$ k $为一个四分之一的数字字段，包含$ \ sqrt {2} $，让$ \ Mathcal {o} \ subseteq k $为订单，以至于$ \ sqrt {2} \ in \ Mathcal {o} $。我们证明$ \ Mathcal {O} $的毕达哥拉斯号最多是5。这证实了Krásenský，Raška和Sgallová的猜想。该证明利用了贝利的规范发生器的基础理论，用于二次晶格上的二元局部领域。
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.
