Ternary quadratic forms over number fields with small class number
type: Item
instance of: scholarly article
title: Ternary quadratic forms over number fields with small class number
zbMATH Open document ID: 1332.11045
author: Markus Kirschmer
author: David Lorch
published in: Journal of Number Theory
publication date: 2015-12-21T00:00:00Z
review text: The authors use the correspondence of ternary quadratic forms over number fields with quaternion orders for the enumeration of all positive definite ternary quadratic forms with class number 1 or 2 over totally real number fields. The method is to enumerate all definite quaternion orders of type number 1 or 2 over totally real number fields using Eichler's mass formula. Furthermore, all definite quaternion orders of ideal class number 1 or 2 are listed.
Mathematics Subject Classification ID: 11E41
Mathematics Subject Classification ID: 16H10
zbMATH DE Number: 6522682
zbMATH Keywords: ternary quadratic forms
zbMATH Keywords: class numbers
zbMATH Keywords: quaternion orders
zbMATH Keywords: type numbers
reviewed by: Meinhard Peters
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.jnt.2014.11.001
OpenAlex ID: W2011508211
cites work: The Magma algebra system. I: The user language
cites work: Zur Zahlentheorie der Quaternionen
cites work: LOCAL CORRECTIONS OF DISCRIMINANT BOUNDS AND SMALL DEGREE EXTENSIONS OF QUADRATIC BASE FIELDS
cites work: Arithmetical quadratic surfaces of genus 0, I.
cites work: A characterisation of Gorenstein orders in quarternition algebras.
cites work: On orders in quaternion algebras
cites work: Definite quaternion orders of class number one
cites work: Q5542154
cites work: Q5578242
cites work: Q5816776
cites work: Zur Zahlentheorie der Quaternionen-Algebren.
cites work: On cubic rings and quaternion rings
cites work: One-class genera of maximal integral quadratic forms
cites work: Single-class genera of positive integral lattices
cites work: Corrigendum: ``Algorithmic enumeration of ideal classes for quaternion orders''
cites work: Q2778950
cites work: Q4541479
cites work: Traces of Eichler-Brandt matrices and type numbers of quaternion orders
cites work: Q3758034
cites work: On the radical idealizer chain of symmetric orders.
cites work: Q5675787
cites work: On Generalized Quaternions
cites work: Ternäre und quaternäre quadratische Formen und Quaternionenalgebren
cites work: Einklassige Geschlechter totalpositiver quadratischer Formen in totalreellen algebraischen Zahlkörpern
cites work: An algorithm for computing modular forms on \(\Gamma_0(N)\)
cites work: Computing isometries of lattices
cites work: Q4414310
cites work: Q5852633
cites work: Arithmétique des algèbres de quaternions
cites work: Enumeration of Totally Real Number Fields of Bounded Root Discriminant
cites work: Characterizing quaternion rings over an arbitrary base
cites work: Identifying the Matrix Ring: Algorithms for Quaternion Algebras and Quadratic Forms
cites work: One-Class Genera of Positive Quadratic Forms in Eight Variables
cites work: Transformations of a Quadratic Form Which Do Not Increase the Class-Number
cites work: One-Class Genera of Positive Quadratic Forms in Seven Variables
cites work: Q5661986
DOI: 10.1016/J.JNT.2014.11.001
description: scientific article; zbMATH DE number 6522682