Mathematical Sciences: Eisenstein Series, Theta Functions and Special Values of L-Functions

该奖项支持马里兰大学帕克分校的史蒂文·库德拉教授在自同构形式方面的研究。库德拉博士的项目是研究两个涉及西塔函数的问题：L函数和算术。第一个问题是关于Siegel Eisenstein级数的Laurent展开式的前两项在某些特殊点上的识别的猜想。第二个是关于Gross和Zagier结果的三重L函数的一个类比，它将GL(2)上全纯尖点形式的标准L函数的导数与模曲线的Jacobian上Heegner点的高度配对联系起来。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产生了现代数学的几个分支，其中模和自同构形的研究是最活跃的之一。这一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 Steven Kudla of the University of Maryland at College Park. Dr. Kudla's project is to work on two problems involving theta functions, L-functions, and arithmetic. The first of these problems concerns a conjecture about the identification of the first two terms in the Laurent expansion of the Siegel Eisenstein series at certain special points. The second is concerned with an analogue for the triple L-function of the result of Gross and Zagier that relates the derivative of the standard L-function of a holomorphic cusp form on GL(2) to the height pairing of Heegner points on the Jacobian of the modular curve. 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.