Mathematical Sciences: Automorphic L-Functions and Representation Theory

该奖项支持自守形式的研究， 普渡大学教授Freydoon Shahidi的表征理论 大学Shahidi博士的一个项目是研究 上的拟分裂群上的尖点形式的可能等价性 数字字段，在具有非零傅立叶系数 关于极大幂幺的类属特征标 子组，并且到处都有通用的本地组件。另一 相关的项目是证明某些局部L- 与调和表示相关的功能。 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，但在其使用的几何和分析，它 与其历史根源保持联系。

This award supports the research in automorphic forms and representation theory of Professor Freydoon Shahidi of Purdue University. One of Dr. Shahidi's projects is to study the possible equivalence, for a cusp form on a quasi-split group over a number field, between having a non-zero Fourier coefficient with respect to a generic character of a maximal unipotent subgroup, and having generic local components everywhere. Another related project is to prove the holomorphy of certain local L- functions related to tempered representations. 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.