Mathematical Sciences: RUI: Binary Additive Problems Involving Primes and Other Topics in Analytic Number Theory

这笔经费支持丹尼尔·戈德斯顿教授在分析数论方面的研究。Goldston教授将使用von Mangoldt lambda函数的一种新的近似来研究以前用圆法检验过的问题。他还将研究ζ函数零点和西格尔零点的对相关关系。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，但是随着现代分析数论学家的工作，这个领域有了新的重生。

This grant supports the research of Professor Daniel Goldston in analytic number theory. Professor Goldston will use a new approximation to the von Mangoldt lambda function to study problems that were previously examined with the circle method. He will also study pair correlations of the zeros of zeta functions and Siegel zeros. 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.