Mathematical Sciences: Convolution Orthogonality

数学科学：卷积正交性

• 批准号: 9102906
• 负责人: Brent Smith
• 金额: $ 5.17万
• 依托单位: Kansas State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-15 至 1994-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102906&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Convolution; Orthogonality

This grant supports the research of Professor B. Smith to work on general Tauberian theorems and their applications to number theory. In particular, he wishes to develop a Tauberian theorem that would be applicable to the estimation of integrals that arise in the twin prime conjecture. The field of analytic number theory applies to the discrete realm of the whole numbers the techniques of analysis. These techniques, dependent on the notions of continuity and limit, originated with the calculus. The idea of using continuous methods to investigate the discrete is two centuries old, but with the work of the modern analytic number theorists, the field has had a new rebirth.

这笔赠款支持B教授的研究。史密斯工作 关于一般Tauberian定理及其在数的应用 理论 特别是，他希望发展一个陶伯定理， 这将适用于估计积分， 孪生素数猜想 解析数论领域适用于离散 数字分析的技巧。 这些 技术，依赖于连续性和极限的概念， 起源于微积分 使用连续方法的想法 研究离散性已经有两个世纪的历史了， 在现代解析数论中，这个领域有了一个新的 重生