Mathematical Sciences: Regularized Products, Heat Kernal Analysis and Analytic Number Theory

数学科学：正则化积、热核分析和解析数论

• 批准号: 9307023
• 负责人: Jay Jorgenson
• 金额: $ 8万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9307023&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Regularized; Products; Heat

The problems that are to be addressed in this project lie in the general area of spectral theory and number theory, with particular interest in trace formulae, explicit formulae and prime number theorems, and various analytic and arithmetic aspects of Arakelov theory. The proposed research is very broad, involving analysis, number theory, and algebraic geometry. This research uses the techniques of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.

这个项目要解决的问题在于谱论和数论的一般领域，特别是对迹公式、显式公式和素数定理以及阿拉克洛夫理论的各种分析和算术方面的兴趣。拟议的研究非常广泛，涉及分析、数论和代数几何。这项研究使用了代数几何的技术，这是现代数学中最古老的部分之一，但在过去的25年里取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，该领域不仅使用代数的方法，而且使用分析和拓扑学的方法，反过来，在这些领域以及物理、理论计算机科学和机器人中也找到了应用。