Mathematical Sciences: RUI: Topics in Analytic Number TheoryRelated to the Distribution of Primes

数学科学：RUI：与素数分布相关的解析数论主题

• 批准号: 9003329
• 负责人: Daniel Goldston
• 金额: $ 4.39万
• 依托单位: San Jose State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003329&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Topics; Analytic

This award supports the research in analytic number theory of Professor Daniel Goldston of San Jose State University. Dr. Goldston's project involves a study of the fine details in the pattern of distribution of prime numbers. He plans to examine the Hardy-Littlewood circle method and its application to the study of small gaps between primes and the exceptional sets for the Goldbach conjecture; the Riemann zeta function as a tool for studying large gaps between primes; Maier's method and differential delay questions; and connections of these methods with the emerging understanding of the duality between primes and zeros of zeta functions. 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 Goldston, the field has had a new rebirth.

该奖项支持圣何塞州立大学丹尼尔·戈德斯顿教授在解析数论方面的研究。戈德斯顿博士的项目涉及对质数分布模式中的细节进行研究。他计划研究Hardy-Littlewood圆法及其在研究素数和Goldbach猜想例外集之间的小间隙中的应用；Riemann Zeta函数作为研究素数之间大间隙的工具；迈尔法和微分延迟问题；以及这些方法与Zeta函数的素数和零点之间的对偶性的新兴理解之间的联系。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数的想法已经有两个世纪的历史了，但随着戈德斯顿教授等现代分析数论家的工作，该领域获得了新的新生。