Mathematical Sciences: Problems in Analytic Number Theory

数学科学：解析数论问题

• 批准号: 9401702
• 负责人: Hugh Montgomery
• 金额: $ 10.12万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401702&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Analytic; Number

Montgomery This award funds the research in analytic number theory of Professor Hugh Montgomery. Prof. Montgomery will study a number of outstanding problems in multiplicative and additive number theory including the Riemann Hypothesis. In one part of the project he hopes to construct a general technique for determining optimal sieve methods. Such a technique would have wide application. The field of analytic number theory applies the techniques of calculus to the discrete realm of the whole numbers. Calculus was developed to aid the analysis of continuous mathematical objects. The idea of using continuous methods to investigate discrete objects is two centuries old, but with the work of the modern analytic number theorists such as Professor Montgomery, the field has had a new rebirth. ***

蒙哥马利 该奖项资助休蒙哥马利教授的解析数论研究。 蒙哥马利教授将研究乘法和加法数论中的一些突出问题，包括黎曼假设。 在该项目的一部分，他希望构建一个通用的技术，以确定最佳的筛选方法。 这种技术将有广泛的应用。 解析数论领域将微积分的技术应用于整数的离散领域。 微积分的发展是为了帮助分析连续的数学对象。 使用连续方法研究离散对象的想法已有两个世纪的历史，但随着蒙哥马利教授等现代解析数论家的工作，该领域已经获得了新的重生。 ***