Mathematical Sciences: The Theta Correspondence and Central Derivatives of L-Functions

数学科学：L 函数的 Theta 对应关系和中心导数

• 批准号: 9302539
• 负责人: Stephen Kudla
• 金额: $ 6.44万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302539&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theta; Correspondence; Central

The principal investigator will focus in on some problems involving theta functions, the Siegel-Weil formula, values and derivatives of L-functions and algebraic cycles on Shimura varieties. A generalization of the work of Waldspurger and of Gross and Zagier will be attempted, together with problems that concern the completion of the theory of the standard L-function for classical groups via the doubling method of Piatetski-Shapiro and Rallis. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.

首席研究者将重点研究涉及theta功能的一些问题，siegel-weil公式，l功能和代数周期的shimura品种的值和衍生物。 将尝试对Waldspurger和Gross和Zagier的工作的概括，以及通过Piatetski-Shapiro和Rallis的加倍方法对古典群体的标准L功能理论完成的问题。 这是数字理论领域的研究。 数字理论始于整个数字和问题，例如一个整数的划分。 它是数学最古老的领域之一，最初是出于纯粹的审美原因而追求的。 但是，在过去的半个世纪中，它已成为开发用于计算机科学的新算法的重要工具，并为电子设备纠正新的错误代码。