Mathematical Sciences: Classical Analysis, Number Theory and Quantum Chaos

数学科学：经典分析、数论和量子混沌

• 批准号: 9424368
• 负责人: Dennis Hejhal
• 金额: $ 10.5万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9424368&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Classical; Analysis; Number

Hejhal DMS-9424368 Hejhal will use high-performance computers to investigate three topics: analytic number theory, automorphic forms and the Selberg trace formalism, and quantum chaos. In number theory, the PI will be seeking a better understanding of the zeros of various kinds of zeta functions. He will be focusing on the asymptotic spacing pattern in the zeros and seeking to reconcile this with certain statistical ensembles arising in random matrix theory. This work has important application to fundamental and long-standing questions in number theory. It also leads to new uses of supercomputing in the more theoretical areas of mathematical analysis, both as an experimental tool and one which can give sharp probability estimates in situations where precise information is too difficult to extract from the functions definitions.

Hejhal DMS-9424368 Hejhal将使用高性能计算机研究三个主题：解析数论、自同构形和塞尔伯格迹形式论，以及量子混沌。在数论中，PI将寻求更好地理解各种Zeta函数的零点。他将专注于零点的渐近间隔模式，并寻求将其与随机矩阵理论中出现的某些统计系综相协调。这项工作对数论中的基本和长期存在的问题有重要的应用。它还导致了超级计算在数学分析的更多理论领域的新用途，既作为一种实验工具，也作为一种工具，可以在难以从函数定义中提取准确信息的情况下给出精确的概率估计。