Mathematical Sciences: Gauss Sums, Zeta and Gamma Functions in Arithmetic of Function Fields

塔库尔教授将研究与函数域的算术有关的几个问题。特别是，他将研究Carlitz Zeta函数的特殊值的算术性质以及函数域中的Gauss和和Gamma函数的类似物。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。

Professor Thakur will work on several problems connected with the arithmetic of function fields. In particular, he will study the arithmetic properties of special values of the Carlitz zeta function as well as analogues of Gauss sums and gamma functions in the function field case. 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.