Mathematical Sciences: Diophantine Inequalities and Multiplicative Number Theory

数学科学：丢番图不等式和乘法数论

• 批准号: 9200835
• 负责人: Roger Baker
• 金额: $ 9万
• 依托单位: Brigham Young University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9200835&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Diophantine; Inequalities; Multiplicative

This grant supports the research of Professor Roger Baker in analytic number theory. Professor Baker will study a broad class of problems in Diophantine inequalities around Weyl sums. He will also study exponential sums via the values of Dirichlet polynomials and sieves. 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, the field has had a new rebirth.

这笔赠款支持罗杰·贝克教授在解析数论方面的研究。贝克教授将研究关于Weyl和的丢番图不等式中的一大类问题。他还将通过Dirichlet多项式和筛子的值来研究指数和。解析数论的领域适用于整数的离散领域，分析技术依赖于连续性和极限的概念，起源于微积分。使用连续方法研究离散的想法已经有两个世纪的历史了，但随着现代解析数学家的工作，该领域获得了新的新生。