论文标题
相对于原始元素，代数数的最小程度
Minimal Degrees of Algebraic Numbers with respect to Primitive Elements
论文作者
论文摘要
给定一个数字字段$ l $，我们根据选择$ l $的原始元素来定义l $中代数数$ v \的度。我们提出了计算$ L $中代数数字最小程度的问题，并以$ 4 $ galois扩展名的$ \ Mathbb {q} $和Triquadratic数字字段来检查这些值。我们表明，计算三级数字字段中非理性元素的最低程度与解决经典的二只问题（例如一致数字问题）密切相关，并了解椭圆曲线的各种算术特性。
Given a number field $L$, we define the degree of an algebraic number $v \in L$ with respect to a choice of a primitive element of $L$. We propose the question of computing the minimal degrees of algebraic numbers in $L$, and examine these values in degree $4$ Galois extensions over $\mathbb{Q}$ and triquadratic number fields. We show that computing minimal degrees of non-rational elements in triquadratic number fields is closely related to solving classical Diophantine problems such as congruent number problem as well as understanding various arithmetic properties of elliptic curves.
