On small discriminants of number fields of degree 8 and 9

DOI10.5802/jtnb.1131zbMath1460.11127arXiv1910.07208OpenAlexW3097774090MaRDI QIDQ2211028

Francesco Battistoni

Publication date: 10 November 2020

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.07208

zbMATH Keywords

small discriminantHunter-Pohst-Martinet theoremsignature of a number field

Mathematics Subject Classification ID

Other number fields (11R21) Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29)

Uses Software

• PARI/GP
• LMFDB

Cites Work

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• Sharp lower bounds for regulators of small-degree number fields
• Valeurs minima du discriminant pour certains types de corps de degré 7
• Corps sextiques primitifs. (Primitive sextic fields)
• Petits discriminants des corps de nombres totalement imaginaires de degré 8. (Small discriminants of totally imaginary eight-degree number fields)
• On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields
• A fast algorithm for polynomial factorization over \(\mathbb Q_p\)
• The minimum discriminant of number fields of degree 8 and signature \((2,3)\)
• Constructing transitive permutation groups.
• The minimum discriminant of totally real octic fields
• Corps sextiques contenant un corps cubique (III)
• The Computation of Sextic Fields with a Quadratic Subfield
• Discriminant Minimal Et Petits Discriminants Des Corps De Nombres De Degre 7 Avec Cinq Places Reelles
• The Computation of Sextic Fields with a Cubic Subfield and no Quadratic Subfield
• Corps sextiques primitifs (IV)
• Non-primitive number fields of degree eight and of signature (2,3), (4,2), and (6,1) with small discriminant
• Tables of octic fields with a quartic subfield
• Enumeration of Quartic Fields of Small Discriminant
• A Table of Quintic Number Fields
• Imprimitive Ninth-Degree Number Fields with Small Discriminants
• A fast algorithm to compute cubic fields
• Construction de polynômes de petits discriminants
• A Database for Field Extensions of the Rationals
• Advanced Topics in Computional Number Theory
• On the density of discriminants of cubic fields. II
• Corps sextiques contenant un corps quadratique (I)
• Corps sextiques contenant un corps quadratique (II)
• Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results

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