L-Functions and Spectral Problems

L 函数和谱问题

• 批准号: 9970386
• 负责人: Peter Sarnak
• 金额: $ 30万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970386&HistoricalAwards=false
• 关键词: Functions; Spectral; Problems

Sarnak9970386The proposed project concerns zeroes of L-functions. We intend to investigate the fine structure of these zeroes for families of L-functions. They are intimately connected to random matrix theory and symmetry groups, and for certain families, arithmetical questions such as ranks of Abelian varieties. Some of what we set out to establish has been discovered through computer experiments.Our general area of research is number theory and related topics. Also entering into these works are some ideas from mathematical physics, in particular symmetry properties and universalities associated with random matrix ensembles.

Sarnak9970386拟议的项目涉及 L 函数的零点。 我们打算研究 L 函数族的这些零点的精细结构。 它们与随机矩阵理论和对称群以及某些族的算术问题（例如阿贝尔簇的等级）密切相关。 我们着手建立的一些内容是通过计算机实验发现的。我们的一般研究领域是数论和相关主题。 这些作品还涉及数学物理学的一些思想，特别是与随机矩阵系综相关的对称性和普遍性。