Mathematical Sciences: Zeta Functions and Transfer Operators

数学科学：Zeta 函数和传递算子

• 批准号: 9205110
• 负责人: Isaac Efrat
• 金额: $ 6.9万
• 依托单位: University of Maryland, College Park
• 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: 1992-06-15 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9205110&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Zeta; Functions; Transfer

Professor Efrat will work on several problems connected with automorphic forms. In particular, he will study the interplay between dynamical systems on the unit interval and zeta functions attached to Riemann surfaces. In particular, to explore consequences of the connection between zeta functions of modular surfaces and the determinant of the transfer operator for the corresponding dynamical system. Automorphic forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.

Efrat教授将研究与以下方面有关的几个问题： 自守型 特别是，他将研究 单位区间上的动力系统与zeta函数 Riemann曲面的一种。 特别是， 模的zeta函数之间联系的结果 表面和转移算子的行列式， 相应的动力系统。 自守形式产生于非欧几里德几何， 世纪中期。 数学家和 物理学家早就意识到， 基本的重要性是非欧几里德在其基本性质。 此字段主要涉及有关 整数，但在其使用的几何和分析，它 保留了与其历史根源的联系，从而与问题 从理论物理中的规范理论， 信息论中的编码理论