Mathematical Sciences: Arithmetic of Automorphic Forms on Unitary Groups in Three Variables

数学科学：三变量酉群自守形式的算术

• 批准号: 8905578
• 负责人: Jonathan Rogawski
• 金额: $ 5.71万
• 依托单位: University of California-Los Angeles
• 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 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8905578&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetic; Automorphic; Forms

This award supports the research in Automorphic Forms by Professor Jonathan Rogawski of the University of California at Los Angeles. Dr. Rogawski's project is to continue his investigation of the relations between Number Theory and the theory of automorphic forms on unitary groups in three variables. He plans three interrelated lines of research: The first involves a continuation of his collaboration with S. Gelbart on the representation of the L-function by an integral of Rankin-Shimura type. The second concerns p-adic families of automorphic representations on U(3) and their relation with Galois representations. The third is the investigation of period relations, special values of L-functions, and the Beilinson conjectures for Shimura varieties associated to U(3). 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.

该奖项支持加州大学洛杉矶分校 Jonathan Rogawski 教授在自同构方面的研究。 Rogawski 博士的项目是继续研究数论和三变量酉群自守形式理论之间的关系。 他计划进行三个相互关联的研究方向：第一个涉及继续与 S. Gelbart 合作，通过 Rankin-Shimura 型积分来表示 L 函数。第二个涉及 U(3) 上的自守表示的 p 进族及其与伽罗瓦表示的关系。第三个是对周期关系、L 函数的特殊值以及与 U(3) 相关的 Shimura 簇的 Beilinson 猜想的研究。 非欧几里得平面几何始于 19 世纪初，最初是作为一种数学好奇心，但到了该世纪末，数学家们意识到许多具有根本重要性的物体在其基本性质上都是非欧几里得的。 对非欧几里得平面几何的详细研究催生了现代数学的几个分支，其中模和自同构形式的研究是最活跃的之一。 该领域主要关注有关整数的问题，但在几何和分析的使用中，它保留了与其历史根源的联系。