Mathematical Sciences: Kloosterman Sums and p-adic Differential Equations

数学科学：Kloosterman 和与 p 进微分方程

• 批准号: 8903322
• 负责人: Marvin Wunderlich
• 金额: --
• 依托单位: National Security Agency
• 依托单位国家: 美国
• 项目类别: Interagency Agreement
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-05-15 至 1991-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903322&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Kloosterman; Sums; adic

This award supports the research in Algebraic Geometry of Dr. Richard Crew of the University of Minnesota. His research will center on the study of Kloosterman sums by geometric methods, and in particular, he will investigate the monodromy groups arising from certain p-adic differential equations that come from these sums. This research is work in the Algebraic Geometry of finite characteristic. Although the field originated with notions of continuously varying geometric structures like lines and planes, in this context the Discrete takes over, and methods akin to those from the theory of whole numbers are most useful. Reciprocally, the algebraic geometry of finite characteristic is now having great influence on the Theory of Numbers, and is finding application in Computer Science and Coding Theory.

该奖项支持明尼苏达大学理查德·克鲁斯博士在代数几何方面的研究。他的研究将集中于用几何方法研究Krousterman和，特别是，他将研究由这些和产生的某些p-进微分方程式所产生的单调群。本研究是在有限特征的代数几何中进行的。虽然这个领域起源于像线和面这样不断变化的几何结构的概念，但在这种情况下，离散的概念占据了主导地位，类似于整数理论的方法是最有用的。反过来，有限特征的代数几何现在对数论产生了很大的影响，并在计算机科学和编码理论中得到了应用。