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; 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.

该奖项支持马里兰州大学公园大学的史蒂文·库德拉（Steven Kudla）教授的汽车形式的研究。库德拉（Kudla）博士的项目是解决涉及theta功能，l功能和算术的两个问题。这些问题中的第一个涉及关于在Siegel Eisenstein系列在某些特殊点上的Laurent扩展中对前两个术语识别的猜想。第二个与GL（2）上的holomorthic cusp形式的标准L功能的衍生物与Heegner点的高度配对在模块化曲线的jacobian上的高度配对。 非欧几里得平面的几何形状始于十九世纪初，是一种数学好奇心，但是到那个世纪末，数学家意识到许多基本重要性的对象在基本本质上都是非欧国人。 非欧几里得平面几何形状的详细研究引起了现代数学的几个分支，其中模块化和自动形式的研究是最活跃的形式之一。 该领域主要关注有关整数的问题，但是在使用几何和分析时，它保留了与历史根源的联系。