arXiv subjects
Publications and source records attributed to Moulay Ahmed Hajjami.
Let $p\equiv 1\pmod{8}$ and $q\equiv7\pmod 8$ be two prime numbers. The purpose of this paper is to compute the unit group of the fields $\KK=\QQ(\sqrt 2, \sqrt{p}, \sqrt{q} )$ and give their $2$-class numbers.
The aim of this paper is to give some properties of Hilbert genus fields and construct the Hilbert genus fields of the fields $L_{m,d}:=\mathbb{Q}(ζ_{2^m},\sqrt{d})$, where $m\geq 3$ is a positive integer and $d$ is a square-free integer whose prime divisors are congruent to $\pm 3\pmod 8$ or $9\pmod{16}$.
Let $p$ be a prime number such that $p=2$ or $p\equiv 1\pmod 4$. Let $\varepsilon_p$ denote the fundamental unit of $\mathbb{Q}(\sqrt{p})$ and let $a$ be a positive square-free integer. In the present paper, we construct the Hilbert genus field of the real cyclic quartic fields $\mathbb{Q}(\sqrt{a\varepsilon_p\sqrt{p}})$.
Let $p$ be a prime number such that $p=2$ or $p\equiv 1\pmod 4$. Let $\varepsilon_p$ denote the fundamental unit of $\mathbb{Q}(\sqrt{p})$ and let $a$ be a positive square-free integer. The main aim of this paper is to determine explicitly the Hilbert genus field of the imaginary cyclic quartic fields of the form $\mathbb{Q}(\sqrt{-a\varepsilon_p\sqrt{p}})$.