Integral Quadratic Forms and Related Topics

积分二次形式及相关主题

• 批准号: 0138524
• 负责人: Wai Kiu Chan
• 金额: $ 5.64万
• 依托单位: Wesleyan University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0138524&HistoricalAwards=false
• 关键词: Integral; Quadratic; Forms; Related; Topics

AbstractWai Kiu ChanThis grant supports the research of the principal investigator andhis colleagues on the arithmetic theory of integral quadraticforms and related topics. They will work on the representationtheory of positive definite quadratic forms, the almost strongapproximation properties of simply connected algebraic groups ofcompact types, and the classification of quaternary quadraticforms with improper automorphism groups by their degree two thetaseries.Quadratic forms are homogenous polynomials of degree two in manyvariables. This research concerns the number theoretic problemswhich arises from deciding which integers can be values of thequadratic forms when the variables are replaced by integers. Itfalls into the area of number theory which is among the oldestbranches of mathematics. Nowadays, quadratic forms and otherkinds of number theory become indispensable tools in communicationsciences, data transmission and processing, construction of errorcorrecting codes, and cryptography in information technology.

陈伟翘本基金资助主要研究者及其同事在积分二次型的算术理论及相关课题上的研究。 他们将致力于正定二次型的表示理论，紧致型单连通代数群的几乎强逼近性质，以及四元二次型与不适当的自同构群的分类，二次型是多变量的二次齐次多项式。 本研究涉及当变量被整数替换时，决定哪些整数可以是二次型的值所产生的数论问题。 它属于该地区的数论这是其中最古老的分支数学。 如今，二次型和其他类型的数论成为通信科学、数据传输和处理、纠错码构造以及信息技术中的密码学中不可或缺的工具。