Hilbert genus fields of some number fields with high degrees

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 $\pm 3(\mathrm{mod}8)$ or $9(\mathrm{mod}16)$.

11 pages, published in Acta Mathematica Vietnamica (2022)

References in corpus (1)

• On Hilbert genus fields of imaginary cyclic quartic fields