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Hilbert Genus Fields of Some Number Fields with High Degrees
Mohamed Mahmoud Chems-Eddin
,
Moulay Ahmed Hajjami
,
Mohammed Taous
Abstract
The aim of this paper is to give some properties of Hilbert genus fields and construct the Hilbert genus fields of the fields $L_{m,d}:=\mathbb {Q}(\zeta _{2^{m}},\sqrt {d})$, where $m \ge 3$ is a positive integer and $d$ is a square-free integer whose prime divisors are congruent to $\pm 3$ (mod 8) or 9 (mod 16).