Constructing complete tables of quartic fields using Kummer theory

DOI10.1090/S0025-5718-02-01452-7zbMath1081.11081MaRDI QIDQ4794652

Michel Olivier, Francisco Diaz y Diaz, Henri Cohen

Publication date: 19 February 2003

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

quartic extensionscomputer solution of Diophantine equationsclass numbers, class groups, discriminants

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29)

Related Items

Sharp lower bounds for regulators of small-degree number fields ⋮ Counting discriminants of number fields ⋮ Primes in the Chebotarev density theorem for all number fields (with an appendix by Andrew Fiori) ⋮ Computational Number Theory, Past, Present, and Future ⋮ Mod 4 Galois representations and elliptic curves ⋮ Shimura curves of genus at most two

Cites Work

• Counting discriminants of number fields
• The Computation of Sextic Fields with a Quadratic Subfield
• On the Computation of Totally Real Quartic Fields of Small Discriminant
• The Computation of Sextic Fields with a Cubic Subfield and no Quadratic Subfield
• Tables of octic fields with a quartic subfield
• Enumeration of Quartic Fields of Small Discriminant
• A fast algorithm to compute cubic fields
• Computing ray class groups, conductors and discriminants
• Advanced Topics in Computional Number Theory
• On the Density of Discriminants of Cubic Fields
• On the density of discriminants of cubic fields. II
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