On Hilbert genus fields of imaginary cyclic quartic fields

Abstract

Let p be a prime number such that p = 2 or p ≡ 1 (mod 4). Let εp denote the fundamental unit of Q( √ 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( √ −aεp √ p) .