Zeta Functions and L-Functions Over Finite Fields

9622895 wan这笔赠款支持D.wan教授在算术几何方面的工作，特别是函数域的算术问题。他打算研究定义在特征为p的有限域上的仿射代数簇的算术基本群的连续表示上的L函数。他打算研究这些L函数的有理性质、可能的亚纯延拓、整体性和黎曼假设。这个项目属于算术几何的一般领域--一个融合了数论和几何这两个最古老的数学领域的学科。事实证明，这种结合非常有成效--最近解决了几代人经受住的问题。在其众多后果中，有一种是新的纠错码。这种代码对于现代计算机(硬盘)和光盘都是必不可少的。

9622895 Wan This grant supports the work of Professor D. Wan to work in arithmetic geometry specifically problems in the arithmetic of function fields. He intends to study the L-function attached to a continuos representations of the arithmetical fundamental group of an affine algebraic variety defined over a finite field of characteristic p. He intends to study rationality, possible meromorphic continuations, entireness and the Riemann hypothesis for these L-functions. This project falls into the general area of arithmetic geometry - a subject that blends two of the oldest areas of mathematics: number theory and geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.