Mathematical Sciences: Arithmetic of Automorphic Forms

该奖项支持明尼苏达大学保罗·加勒特教授的自同构形式的研究。Garrett博士的工作涉及L函数和Eisenstein级数的积分表示。他计划从事的课题包括：自同构形式作为theta级数的表示准则，艾森斯坦级数和L函数的零极点之间的关系，附加在尖形上的艾森斯坦级数的积分表示，以及具有规定不变性的黑克特征函数的唯一性结果。非欧几里得平面几何始于十九世纪初，最初是一种数学奇闻，但到那个世纪末，数学家们已经意识到许多具有根本重要性的物体本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已经形成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。这个领域主要涉及关于整数的问题，但在几何和分析的使用中，它保留了与其历史根源的联系。

This award supports the research in Automorphic Forms of Professor Paul Garrett of the University of Minnesota. Dr. Garrett's work is concerned with integral representations of L- functions and Eisenstein series. Among the topics he plans to work on are: criteria for expressibility of automorphic forms as theta series, relations between zeros and poles of Eisenstein series and L-functions, integral representations of Eisenstein series attached to cuspforms, and uniqueness results for Hecke eigenfunctions with prescribed invariance. 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.