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. ***

Sczech 该奖项资助 Robert Sczech 教授在解析数论方面的研究。 Sczech 教授计划在整数上维度为 n 的一般线性群的 Eilenberg-MacLane 上同调中明确构造某些爱森斯坦余循环。 这些构造的最终目的是研究数论中特定 L 函数的特殊值。 这是解析数论领域的研究。 数论是对整数性质的研究。 在解析数论中，通过将数字编码为微积分函数来检查整数的属性。 数论是数学最古老的领域之一，但它在选择该学科其他部分的方向方面始终发挥着重要作用。 在过去的半个世纪中，整数的研究变得更加重要，因为该理论已被用来开发计算机科学的新算法和构建新的电子纠错码。 ***