Mathematical Sciences: Gaps Between k-Free Numbers, Finite Differences, and Exponential Sums

数学科学：k-自由数、有限差分和指数和之间的差距

• 批准号: 8903123
• 负责人: Michael Filaseta
• 金额: $ 3.22万
• 依托单位: University of South Carolina at Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903123&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Gaps; Between; Free

This award supports the research in Analytic Number Theory of Professor Michael Filaseta of the University of South Carolina. His project is concerned with gap problems for k-free numbers and in particular for squarefree numbers. His main tool for attacking these problems will be an extension that he has developed to an elementary method of Halberstam and Roth, and to combine this with exponential sum techniques. The field of Analytic Number Theory applies to the discrete realm of the whole numbers the techniques of Analysis, dependent on the notions of continuity and limit, originating in 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 such as Professor Filaseta, the field has had a new rebirth.

该奖项支持南卡罗莱纳大学Michael Filaseta教授在解析数论方面的研究。他的项目是关于无k数，特别是无平方数的间隙问题。他解决这些问题的主要工具将是他对哈伯斯塔姆和罗斯的基本方法的扩展，并将其与指数和技术相结合。解析数论领域应用于整数的离散领域的分析技术，依赖于连续性和极限的概念，起源于微积分。用连续方法研究离散问题的想法已经有两个世纪的历史了，但随着菲拉塞塔教授等现代分析数论家的工作，这个领域有了新的重生。