Zeta Functions and L-Functions Over Finite Fields

9622895万本基金支持万教授在算术几何方面的工作，特别是在函数域的算术问题。他打算研究在特征p的有限域上定义的仿射代数变体的算术基本群的连续表示所附的l -函数。他打算研究这些l -函数的合理性、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，它融合了数学中两个最古老的领域：数论和几何。事实证明，这一组合非常富有成效——最近解决了几代人经受住了考验的问题。其诸多后果之一是新的纠错码。这些代码对现代计算机（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.