Mathematical Sciences: Analytic Number Theory on Groups

数学科学：群的解析数论

• 批准号: 9200716
• 负责人: Dorian Goldfeld
• 金额: $ 20.58万
• 依托单位: Columbia University
• 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: 1992-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9200716&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytic; Number; Theory

Professor Goldfeld will work on several problems connected with automorphic forms. In particular, he will study special values of the derivative of L-functions and determine if a cohomology theory of special values of L-functions can be developed. 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.

戈德菲尔德教授将研究几个问题， 自守形式。 特别是，他将研究特别 值的衍生物的L-函数，并确定如果 L-函数特殊值的上同调理论可以 开发 自守形式起源于非欧几何 在世纪中期。 两位数学家 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