Certain Quartic Fields with Small Regulators Original Research Article

For quartic fields with a quadratic subfield, explicit lower bounds of the regulators are given in terms of the discriminant. Further, these bounds are shown to be in a sense best possible by constructing infinitely many quartic fields with explicit fundamental units whose regulators approach our lower bounds as their discriminants become large. The fields constructed are new families of non-galois fields given by explicit quartic polynomials.