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

该奖项支持自守形式的研究， 加州大学的乔纳森·罗加夫斯基教授在 洛杉矶。Rogawski博士的项目是继续他的 数论与数学关系的探讨 三元酉群的自守形式理论。 他计划进行三条相互关联的研究路线： 这是他与S. Gelbart在 L-函数的Rankin-Shimura积分表示 类型.第二个问题是自守的p进族 U（3）上的表示及其与伽罗瓦的关系 表示。三是考察期 关系，L-函数的特殊值，以及Beilinson 与U（3）相关的Shimura品种的鉴定。 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。

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.