Mathematical Sciences: Gauss Sums, Zeta and Gamma Functions in Arithmetic of Function Fields

数学科学：函数域算术中的高斯和、Zeta 和 Gamma 函数

• 批准号: 9207706
• 负责人: Greg Anderson
• 金额: $ 1.98万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9207706&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Gauss; Sums; Zeta

Professor Thakur will work on several problems connected with the arithmetic of function fields. In particular, he will study the arithmetic properties of special values of the Carlitz zeta function as well as analogues of Gauss sums and gamma functions in the function field case. This project falls into the general area of arithmetic geometry - a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.

Thakur教授将研究与以下方面有关的几个问题： 函数域的算术。 特别是，他将研究 特殊Carlitz zeta值的算术性质 函数以及高斯和和伽马函数的类似物， 功能字段的情况下。 这个项目福尔斯属于算术的一般范畴 几何学-一个融合了两个最古老的领域的主题， 数学：数论和几何。 这种组合有 被证明是非常富有成效的-最近解决了一些问题 经受住了几代人的考验 在其众多后果中， 纠错码 这些准则对现代和 计算机（硬盘）和光盘。