Mathematical Sciences: Arithmetic of Polynomials and Prehomogeneous Vector Spaces

伊古萨教授将研究K-分裂不可约拟齐次向量空间。特别是，他希望在其余情况下完成局部Zeta函数的计算。他还打算研究泛p-进Zeta函数的非标准因子。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 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.