On Hilbert Genus Fields Of Imaginary Cyclic Quartic Fields

Let p be a prime number such that p = 2 or p equivalent to 1 (mod 4). Let epsilon(p) denote the fundamental unit of Q(root p) and let a be a positive square-free integer. The main aim of this paper is to determine explicitly the Hilbert genus field of the imaginary cyclic quartic fields of the form Q(root-a epsilon(p)root p).