Mathematical Sciences: Kloosterman Sums and Traces of Lisse Sheaves as Algebraic Integers

数学科学：Kloosterman 作为代数整数的 Lisse Sheaves 的求和与迹

• 批准号: 9204738
• 负责人: Benji Fisher
• 金额: $ 4.32万
• 依托单位: Columbia University
• 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 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204738&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Kloosterman; Sums; Traces

Professor Fisher will work on the equidistribution theorem for Kloosterman sums. He also hopes to generalize Katz's equidistribution theorem to lisse sheaves with traces in a number field. He also hopes to study numerically the distinctness of Kloosterman sums. 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.

Fisher教授会讲Kloosterman和的等分布定理。他还希望将卡茨的等分布定理推广到数域中带迹的lisse束。他还希望从数值上研究Kloosterman和的特殊性。这个项目属于算术几何的一般领域，它融合了数学中两个最古老的领域：数论和几何。事实证明，这一组合非常富有成效——最近解决了几代人经受住了考验的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机（硬盘）和光盘都是必不可少的。