论文标题
季度和通用二次形式在数字字段上
Quaternions and universal quadratic forms over number fields
论文作者
论文摘要
我们通过使用相关的四元环在完全真实的数字字段上研究二次形式。我们检查了这些四季度残留类环的某些特性，并使用数字的几何形状证明四季度的某些理想包含一个小规范的元素。我们证明，$ x^2+y^2+z^2+w^2+xy+xz+xw $是通用$ \ mathbb {q}（q}（ζ_7+ζ_7^{ - 1}）$，而$ x^2+xy+xy+xy+xy+y^2+z^2+zw+zw+zw+w^2 $代表某些特殊阳性的所有东西。
We study quadratic forms over totally real number fields by using an associated ring of quaternions. We examine some properties of residue class rings of these quaternions and use geometry of numbers to prove that certain ideals of the ring of quaternions contain elements of a small norm. We prove that $x^2+y^2+z^2+w^2+xy+xz+xw$ is universal over $\mathbb{Q}(ζ_7+ζ_7^{-1})$ and that $x^2+xy+y^2+z^2+zw+w^2$ represents all totally positive multiples of certain special elements.
