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

点击翻译按钮获取中文摘要

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.