December 2022 The construction of the Hilbert genus fields of real cyclic quartic fields
Mohamed Mahmoud Chems-Eddin, Moulay Ahmed Hajjami, Mohammed Taous
Funct. Approx. Comment. Math. 67(2): 235-257 (December 2022). DOI: 10.7169/facm/2014

Abstract

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 $\mathbb{Q}(\sqrt{a\varepsilon_p\sqrt{p}})$.

Citation

Download Citation

Mohamed Mahmoud Chems-Eddin. Moulay Ahmed Hajjami. Mohammed Taous. "The construction of the Hilbert genus fields of real cyclic quartic fields." Funct. Approx. Comment. Math. 67 (2) 235 - 257, December 2022. https://doi.org/10.7169/facm/2014

Information

Published: December 2022
First available in Project Euclid: 18 November 2022

MathSciNet: MR4593177
zbMATH: 1514.11069
Digital Object Identifier: 10.7169/facm/2014

Subjects:
Primary: 11R16 , 11R29
Secondary: 11R04 , 11R27 , 11R37

Keywords: Hilbert genus fields , real cyclic quartic fields , unramified extensions

Rights: Copyright © 2022 Adam Mickiewicz University

JOURNAL ARTICLE
23 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.67 • No. 2 • December 2022
Back to Top