Hilbert genus fields of real biquadratic fields (Q5894180)

The authors construct the Hilbert genus field of a real biquadratic number field \(K={\mathbb Q}(\sqrt{p},\sqrt{d})\) with \(p\equiv 1\pmod 4\) or \(p=2\), \(d\) a positive squarefree integer prime to \(p\), and of \(k(\sqrt{P},\sqrt{D})\), where \(k={\mathbb F}_q(T)\), \(P\) is a monic irreducible polynomial of even degree, and \(D\) a monic squarefree polynomial in \({\mathbb F}_q[T]\).