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

该奖项支持在自守形式的研究 马里兰州大学的史蒂文·库德洛教授 公园Kudla博士的项目是研究两个问题， theta函数L函数和算术其中第一个 问题涉及一个猜想的识别 Siegel Eisenstein的Laurent展开式的前两项 在某些特殊的点上。第二个是关于一个 Gross结果的三重L-函数的类似物， Zagier，它将标准L-函数的导数 GL（2）上的一个全纯尖点型与Heegner的高度配对 点的雅可比矩阵的模曲线。 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 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.