Zeta Functions and L-Functions Over Finite Fields

有限域上的 Zeta 函数和 L 函数

• 批准号: 9622895
• 负责人: Daqing Wan
• 金额: $ 6.5万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622895&HistoricalAwards=false
• 关键词: Zeta; Functions; Over; Finite; Fields

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.

小行星9622895 该基金支持D教授的工作。Wan致力于算术几何，特别是函数域的算术问题。他打算研究的L-函数附加到一个连续表示的算术基本组的仿射代数品种定义在有限领域的特点p。他打算研究合理性，可能的亚纯延续，整体性和黎曼假设 对于这些L函数。 这个项目福尔斯属于算术几何的一般领域-一个融合了两个最古老的数学领域：数论和几何的主题。事实证明，这种结合非常富有成效--最近解决了几代人都无法解决的问题。 在它的许多后果是新的纠错码。 这种代码对于现代计算机（硬盘）和光盘都是必不可少的。