The palindromic index -- A measure of ambiguous cycles of reduced ideals without any ambiguous ideal in real quadratic orders
type: Item
instance of: scholarly article
title: The palindromic index -- A measure of ambiguous cycles of reduced ideals without any ambiguous ideal in real quadratic orders
zbMATH Open document ID: 0855.11054
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1997-01-30T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/227596
full work available at URL: jtnb7-2.html
review text: This paper deals with the theory of ambiguous classes of ideals in real quadratic fields. The author's goal is to ``give a complete overview of the subject including a general criterion for an arbitrary real quadratic order (not necessarily maximal) to have ambiguous cycles of ideals (not necessarily invertible) without any ambiguous ideals in them.'' The notion of the ``palindromic index'' of a reduced ideal is introduced to facilitate the formulation of this criterion. Several numerical examples are presented in detail to illustrate the concepts discussed.
reviewed by: Andrew G. Earnest
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R65
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 858574
zbMATH Keywords: palindromic index
zbMATH Keywords: ambiguous classes of ideals
zbMATH Keywords: real quadratic fields
zbMATH Keywords: real quadratic order
zbMATH Keywords: ambiguous cycles of ideals
author: Richard A. Mollin
MaRDI profile type: Publication
OpenAlex ID: W2164398629
cites work: Q5610449
cites work: Q3139838
cites work: Q3351465
cites work: Infrastructure of ambiguous ideal classes of orders of real quadratic fields
cites work: The distance between ideals in the orders of a real quadratic field
cites work: Groupes des classes d'idéaux triviaux
cites work: Class Numbers of Real Quadratic Fields, Continued Fractions, Reduced Ideals, Prime-Producing Quadratic Polynomials and Quadratic Residue Covers
cites work: Ambiguous Classes in Quadratic Fields
cites work: Classification and Enumeration of Real Quadratic Fields Having Exactly One Non-Inert Prime Less Than a Minkowski Bound
cites work: On the Parallel Generation of the Residues for the Continued Fraction Factoring Algorithm
DOI: 10.5802/JTNB.151
description: scientific article; zbMATH DE number 858574