On Hilbert genus fields of imaginary cyclic quartic fields

Let $p$ be a prime number such that $p=2$ or $p\equiv 1\pmod 4$. $\varepsilon_p$ denote the fundamental unit of $\mathbb{Q}(\sqrt{p})$ and let $a$ positive square-free integer. The main aim this paper is to determine explicitly Hilbert genus field imaginary cyclic quartic fields form $\mathbb{Q}(\sqrt{-a\varepsilon_p\sqrt{p}})$.