论文标题
通用二次形式，小规范和数字领域家族的痕迹
Universal quadratic forms, small norms and traces in families of number fields
论文作者
论文摘要
我们获得了关于尚克斯最简单的立方场和其他几个完全真实数字领域的家族的普遍二次形式等级的良好估计。作为主要工具，我们表征了这些字段中的所有不可分解的整数以及小痕迹的重叠元素。我们还确定标准的主要理想数量的渐近数小于判别物的平方根。
We obtain good estimates on the ranks of universal quadratic forms over Shanks' family of the simplest cubic fields and several other families of totally real number fields. As the main tool we characterize all the indecomposable integers in these fields and the elements of the codifferent of small trace. We also determine the asymptotics of the number of principal ideals of norm less than the square root of the discriminant.
