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

数学科学：爱森斯坦级数、Theta 函数和 L 函数的特殊值

• 批准号: 9003109
• 负责人: Stephen Kudla
• 金额: $ 8.04万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003109&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Eisenstein; Series; Theta

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.

该奖项支持马里兰大学帕克分校教授 Steven Kudla 的自守形式研究。 Kudla 博士的项目是解决涉及 theta 函数、L 函数和算术的两个问题。第一个问题涉及对西格尔·爱森斯坦级数的洛朗展开中前两项在某些特殊点上的识别的猜想。第二个涉及 Gross 和 Zagier 结果的三重 L 函数的类比，它将 GL(2) 上全纯尖点形式的标准 L 函数的导数与雅可比行列式上 Heegner 点的高度配对联系起来的模曲线。 非欧几里得平面几何始于 19 世纪初，最初是作为一种数学好奇心，但到了该世纪末，数学家们意识到许多具有根本重要性的物体在其基本性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催生了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之一。 该领域主要关注有关整数的问题，但在几何和分析的使用中，它保留了与其历史根源的联系。