Mathematical Sciences: Automorphic Forms of Galois Type, andthe L-functions of Some Simple Moduli Varieties

数学科学：伽罗瓦型的自守形式和一些简单模簇的 L 函数

• 批准号: 8905251
• 负责人: Dinakar Ramakrishnan
• 金额: $ 7.59万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8905251&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Automorphic; Forms; Galois

This award supports the research on Automorphic Forms of Professor Dinakar Ramakrishnan of the California Institute of Technology. Dr. Ramakrishnan plans to continue his work on cusp forms of arithmetic type on GL(2), and to investigate certain ensuing problems concerning the Shimura varieties attached to GSp(4) and U(4). He also plans to study the cohomology and cycle classes on these varieties with a view to finding examples of the expected relationship to poles and zeros of L-functions. Non-Euclidean plane geometry began in the early nineteenth century as a mathematical curiosity, but by the end of that century, mathematicians had realized that many objects of fundamental importance are non-Euclidean in their basic nature. The detailed study of non-Euclidean plane geometries has given rise to several branches of modern mathematics, of which the study of Modular and Automorphic Forms is one of the most active. 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.

该奖项支持对自守形式的研究 加州医学研究所的迪纳卡尔·拉马克里希南教授 技术. Ramakrishnan博士计划继续他的研究 GL（2）上算术型的形式，并研究某些 随后的问题有关志村品种所附 GSp（4）和U（4）。他还计划研究上同调和循环 类对这些品种，以期找到的例子， 与L函数的极点和零点的期望关系。 非欧平面几何始于19世纪初 世纪作为一个数学的好奇心，但在年底， 世纪，数学家们已经意识到， 基本的重要性是非欧几里德在其基本性质。 对非欧平面几何的详细研究， 上升到现代数学的几个分支，其中 模和自守形式的研究是最活跃的研究之一。 此字段主要涉及有关 整数，但在其使用几何和分析，它 与其历史根源保持联系。