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

主要研究涉及theta函数、Siegel-Weil公式、l函数的值和导数以及Shimura变量上的代数循环等问题。本文将尝试推广Waldspurger、Gross和Zagier的工作，以及通过Piatetski-Shapiro和Rallis的倍增方法完成经典群的标准l函数理论的问题。这是数论领域的研究。数论从整数和诸如整数能被整数整除之类的问题开始。它是数学中最古老的领域之一，最初纯粹出于审美原因而追求它。然而，在过去的半个世纪里，它已经成为开发计算机科学新算法和电子学新纠错码的重要工具。

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.