Unités d'une famille de corps cycliques réels de degré 6 liés à la courbe modulaire \(X_ 1(13)\). (Units of a family of real cyclic fields of degree 6 related to the modular curve \(X_ 1(13))\)
type: Item
instance of: scholarly article
title: Unités d'une famille de corps cycliques réels de degré 6 liés à la courbe modulaire \(X_ 1(13)\). (Units of a family of real cyclic fields of degree 6 related to the modular curve \(X_ 1(13))\)
zbMATH Open document ID: 0664.12004
DOI: 10.1016/0022-314X(89)90051-6
author: Odile Lecacheux
published in: Journal of Number Theory
publication date: 1989-01-01T00:00:00Z
review text: This paper gives a model for the classical modular curve \(X_ 1(13)\) using two functions h and H. The author defines a third function a in terms of h and H and describes modular units. Specializing a to a rational integer, the values of h and H generate a totally real sextic extension K of \({\mathbb{Q}}\). Using all this, the author obtains that in general H-h is a galois generator of the \(unit\quad group\quad of\quad K\quad (mod\quad torsion).\) Finally the paper describes the ramification in K/\({\mathbb{Q}}\).
reviewed by: Roland Gillard
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 11R21
Mathematics Subject Classification ID: 11F03
zbMATH DE Number: 4085763
zbMATH Keywords: modular curve
zbMATH Keywords: \(X_ 1(13)\)
zbMATH Keywords: modular units
zbMATH Keywords: sextic extension
zbMATH Keywords: unit group
MaRDI profile type: Publication
cites work: Units in the modular function field. I. - II: A full set of units. - III: Distribution relations
cites work: The determination of units in real cyclic sextic fields
cites work: Points rationnels de la courbe modulaire \(X_0(169)\)
cites work: Corps euclidiens, unites exceptionnelles et courbes elliptiques
cites work: Q5181799
full work available at URL: 0022-314x(89)90051-6
OpenAlex ID: W2089099946
description: scientific article; zbMATH DE number 4085763