Sum of Kloosterman Sums, Singular Exponential Sums and Their Applications

Kloosterman 和、奇异指数和及其应用

• 批准号: 9988503
• 负责人: Wenzhi Luo
• 金额: $ 7.56万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2003-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9988503&HistoricalAwards=false
• 关键词: Sum; Kloosterman; Sums; Singular; Exponential

The investigator studies the methods of estimating the sum of exponential sums, especially the sum of the Kloosterman sums, which explores the subtle cancellation of the terms and which goes beyond the bounds of Weil and Deligne for exponential sums. The applications of such methodsto two outstanding problems are highlighted. These sums are fundamental objects and arise naturally from a variety of open problems in number theory and harmonic analysis. The investigator studies the optimal way to estimate them, which potentially has strikingapplications to several well known unsolved problems.

研究了指数和的估计方法，特别是Kloosterman和的估计方法，它探索了项的微妙抵消，并超越了Weil和Deligne关于指数和的界。重点介绍了这种方法在两个突出问题上的应用。 这些总和是基本对象，自然产生于数论和调和分析中的各种开放问题。研究人员研究了估计它们的最佳方法，这可能对几个众所周知的未解决的问题具有惊人的应用。