Mathematical Sciences: Number Fields and Prehomogeneous Vector Spaces

这笔拨款支持D·赖特教授和A·尤基教授的研究。他们将致力于与非齐次向量空间相关的Zeta函数理论，以期计算全球场的四次和五次扩张的判别式。他们希望利用这一理论来获得2类三次域的中值定理。这是数论领域的研究。数论始于整数和诸如一个整数被另一个整数整除的问题。它是最古老的数学领域之一，最初是出于纯粹的美学原因。然而，在过去的半个世纪里，它已经成为开发计算机科学的新算法和电子产品的新纠错码的必要工具。

This grant supports the research of Professor D. Wright and A. Yukie. They will work on the theory of zeta functions associated with prehomogeneous vector spaces with a view to calculating the discriminants of quartic and quintic extensions of global fields. They hope to use this theory to obtain mean value theorems for the 2-class number of cubic fields. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.