Mathematical Sciences: Eisenstein Cocycles for Arithmetic Groups and Values of L-functions

数学科学：算术群和 L 函数值的爱森斯坦余循环

• 批准号: 9401843
• 负责人: Robert Sczech
• 金额: $ 6.97万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401843&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Eisenstein; Cocycles; Arithmetic

Sczech This award funds the research of Professor Robert Sczech in analytic number theory. Prof. Sczech plans to explicitly construct certain Eisenstein cocycles in the Eilenberg-MacLane cohomology of the general linear group of dimension n over the integers. The ultimate aim of these constructions is to study the special values of particular L-functions in number theory. This is research in the field of analytic number theory. Number theory is the study of properties of the whole numbers. In analytic number theory properties of whole numbers are examined by encoding numbers into the functions of calculus. Number theory is among the oldest fields of mathematics, yet it has always played an important role in choosing directions for the rest of the subject. Within the last half century, the study of whole numbers has become doubly important as the theory has been used to develop new algorithms for computer science and to construct new error correcting codes for electronics. ***

这个奖项资助了罗伯特·斯切赫教授在解析数论方面的研究。Sczech教授计划在整数上n维一般线性群的Eilenberg-MacLane上同调中显式地构造某些Eisenstein上循环。这些构造的最终目的是研究特殊的L函数在数论中的特殊价值。这是解析数论领域的研究。数论是研究整体数的性质的学科。在解析数论中，整数的性质是通过将数字编码成微积分的函数来检验的。数论是最古老的数学领域之一，但它在选择其他学科的方向方面一直扮演着重要的角色。在过去的半个世纪里，随着整数理论被用于开发计算机科学的新算法和构造电子产品的新纠错码，对整数的研究变得加倍重要。***