Mathematical Sciences: Number Fields and Prehomogeneous Vector Spaces

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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.