Mathematical Sciences: Composition of Sums of Squares; Quadratic Forms and Galois Groups

本课题主要研究二次方程中的两个问题 形式理论第一个问题是关于合成法的存在 求平方和第二个问题考虑的是 域上二次型的行为 特征异于二与伽罗瓦群的类型 它可以在那个领域出现。 这个项目与二次型的经典研究有关 forms.这一领域的早期成就之一是 高斯发现，每个正整数都是 四个正方形。这一领域的重要性不仅体现在数量上 理论，但在几何和数学的相对论。

This project is concerned with two problems in quadratic form theory. The first concerns the existence of composition laws for sums of squares. The second problem considers the connections between the behavior of quadratic forms over a field of characteristic different than two and the types of Galois groups which can arise over that field. This project is related to the classical study of quadratic forms. One of the early achievements in this field is the discovery by Gauss that every positive whole number is the sum of four squares. This area is important not only in pure number theory but in geometry and the mathematics of relativity.