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Hilbert Genus Fields of Some Number Fields with High Degrees

Mohamed Mahmoud Chems-Eddin , Moulay Ahmed Hajjami , $icon-email$ 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 $L_{m, d} := Q (ζ_{2^{m}}, \sqrt{d})$ , where $m \geq 3$ 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).

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Hilbert Genus Fields of Some Number Fields with High Degrees

Abstract