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

该奖项支持圣何塞州立大学Daniel Goldston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的精细细节的研究。他计划检验Hardy-Littlewood圆方法及其在研究质数之间的小间隙和哥德巴赫猜想的例外集方面的应用；黎曼ζ函数作为研究素数之间大间隙的工具；Maier方法与微分时滞问题以及这些方法与对函数的素数和零的对偶性的理解之间的联系。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，但是随着像Goldston教授这样的现代分析数论家的工作，这个领域有了新的重生。

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.