Minimum Discriminants of Imprimitive Decic Fields

Abstract

In this paper, we compute the minimum discriminants of imprimitive degree-10 fields for different combinations of Galois group and signature. We use class field theory when there is a quintic subfield, and a Martinet search in the more difficult case in which there is only a quadratic subfield.

Keywords:

• Number field
• global field
• minimum discriminiant