On quadratic fields with large 3-rank

DOI10.1090/S0025-5718-04-01632-1zbMath1051.11055MaRDI QIDQ4813624

Karim Belabas

Publication date: 13 August 2004

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

zbMATH Keywords

quadratic field3-rankcubic field

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Quadratic extensions (11R11) Algebraic number theory computations (11Y40) Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29)

Related Items (14)

Counting discriminants of number fields ⋮ Quadratic p-ring spaces for counting dihedral fields ⋮ Secondary terms in counting functions for cubic fields ⋮ Tabulation of Cubic Function Fields with Imaginary and Unusual Hessian ⋮ Shintani’s zeta function is not a finite sum of Euler products ⋮ Error estimates for the Davenport-Heilbronn theorems ⋮ Construction of hyperelliptic function fields of high three-rank ⋮ DISCRIMINANTS CUBIQUES ET PROGRESSIONS ARITHMÉTIQUES ⋮ Bandwidth-efficient threshold EC-DSA ⋮ A database of number fields ⋮ Tabulation of cubic function fields via polynomial binary cubic forms ⋮ Quadratic fields with a class group of large 3-rank ⋮ On calculating the number \(N(D)\) of global cubic fields \(F\) of given discriminant \(D\) ⋮ Computing quadratic function fields with high 3-rank via cubic field tabulation

Uses Software

• PARI/GP

Cites Work

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• A construction for irregular discriminants
• Seminar on complex multiplication. Seminar held at the Institute for Advanced Study, Princeton, N.J., 1957--58
• On unramified Galois extensions of quadratic number fields
• Density of cubic field discriminants
• Multiplicites of Dihedral Discriminants
• Class Groups of Complex Quadratic Fields
• On Totally Real Cubic Fields
• On the 3-Sylow Subgroup of the Class Group of Quadratic Fields
• Quadratic fields with special class groups
• On Some Families of Imaginary Quadratic Fields
• Reduction of Binary Cubic and Quartic Forms
• Courbes modulaires et 11-rang de corps quadratiques
• A fast algorithm to compute cubic fields
• Advanced Topics in Computional Number Theory
• On the density of discriminants of cubic fields. II
• On the Class-Number of Binary Cubic Forms (I)

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