Mathematical Sciences: Arithmetic of Polynomials and Prehomogeneous Vector Spaces

点击翻译按钮获取中文摘要

Professor Igusa will study the K-split irreducible pre- homogeneous vector spaces. In particular, he wishes to complete the calculations for the local zeta functions in the remaining cases. He also intends to investigate non-standard factors of universal p-adic zeta 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.