Mathematical Sciences: Composition Laws For Sum Of Square

数学科学：平方和的复合定律

• 批准号: 8908258
• 负责人: Tara Smith
• 金额: $ 1.2万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1990-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8908258&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Composition; Laws; Sum

This project is concerned with the existence of composition laws for sums of squares. The principal investigator will determine for which positive integers r,s, and n one can write the product of a sum of r squares times a sum of s squares as a sum of n squares. The problem will be approached using algebra, combinatorics and topology. This project is related to the classical study of quadratic forms. One of the early acheivements 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.

该项目涉及平方和的复合定律的存在性。主要研究者将确定哪些正整数 r、s 和 n 可以将 r 平方和乘以 s 平方和的乘积写为 n 平方和。该问题将使用代数、组合学和拓扑学来解决。 该项目与二次形式的经典研究有关。该领域的早期成就之一是高斯发现每个正整数都是四个平方和。这个领域不仅在纯数论中很重要，而且在几何和相对论数学中也很重要。