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

该奖项支持分析数论的研究 南方大学的迈克尔·菲拉塞塔教授 卡罗莱纳。他的项目是关于无k的间隙问题 数字，特别是无平方数。他的主要工具 来解决这些问题， 发展到一个基本的方法Halberloven和罗斯，并 联合收割机将其与指数求和技术相结合。 解析数论的领域适用于离散的 分析的技术，依赖于 关于连续性和极限的概念，起源于微积分。 使用连续方法研究离散的 已经有两个世纪的历史了，但是随着现代分析学家的工作， 一些理论家，如Filaseta教授，该领域已经有了一个 新生

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.