Mathematical Sciences: The Twisted Trace Formula and Cubic Non Normal Extensions

数学科学：扭曲迹公式和三次非正规扩展

• 批准号: 9201741
• 负责人: Jeffrey Stopple
• 金额: --
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard 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=9201741&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Twisted; Trace; Formula

Professor Stopple will work on a new way to look at the trace of Hecke eigenforms on GL(3) by generalizing an idea of Zagier on the trace formula for Hecke operators. He will then apply this trace formula to the case of non-normal cubic extensions of the rationals. 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.

Stopple教授将通过推广Zagier关于Hecke算子迹公式的想法，研究GL（3）上Hecke本征形的迹。然后，他将这个迹公式应用于有理数的非正规三次扩张的情况。自守形式产生于世纪中期的非欧几里德几何。因此，数学家和物理学家早就认识到，许多具有根本重要性的对象在其基本性质上是非欧几里德的。这一领域主要关注的是关于整数的问题，但在几何和分析的应用中，它保留了与其历史根源的联系，从而与理论物理中的规范理论和信息论中的编码理论等不同领域的问题保持联系。