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

首席研究员将专注于一些问题 包括theta函数，Siegel-Weil公式，值和 L-函数的导数与Shimura上的代数圈 品种 一个概括的工作Waldspurger和 Gross和Zagier将被尝试，以及 关于标准L-函数理论的完善， 经典群通过Piatetski-Shapiro的加倍方法， 拉利斯 这是数论领域的研究。 Number 理论开始于整数和问题，如 一个整数被另一个整数整除。 它是其中的 最古老的数学领域，它最初是追求 纯粹的美学原因。 然而，在过去的半个世纪里， 它已经成为开发新算法的重要工具， 计算机科学和新的电子纠错码。

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.