an:03920602
Zbl 0576.12008
Vaughan, Theresa P.
The construction of unramified cyclic quartic extensions of \({\mathbb{Q}}(\sqrt{m})\)
EN
Math. Comput. 45, 233-242 (1985).
00150854
1985
j
11R23 11R37 11R21 11R11
cyclic quartic extensions; unramified extensions; dihedral field; discriminant factors; Hilbert class field
The author studies the dihedral field K for which K/\({\mathbb{Q}}(\sqrt{m})\) is unramified and cyclic of degree 4. Arithmetic conditions on m are given by analyzing the discriminant factors. [See the author's earlier paper, Math. Comput. 40, 685-707 (1983; Zbl 0527.12006).] Illustrations include the cases \({\mathbb{Q}}(\sqrt{-14})\), \({\mathbb{Q}}(\sqrt{-46})\), etc., where K is the Hilbert class field.
Harvey Cohn
Zbl 0527.12006