New types of quadratic fields having three invariants divisible by 3

DOI10.1016/0022-314X(72)90027-3zbMath0265.12001OpenAlexW1976198404MaRDI QIDQ2562210

Daniel Shanks

Publication date: 1972

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-314x(72)90027-3

zbMATH Keywords

discriminantsclass groups generated by quartics

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class numbers, class groups, discriminants (11R29)

Related Items (12)

Using elliptic curves to produce quadratic number fields of high three-rank ⋮ Class pairings and isogenies on elliptic curves ⋮ Algebraic number fields ⋮ Cubic fields, a congruential criterion for Scholz's theorem and new real quadratic fields with 3-rank equal to 4 ⋮ Extensions abéliennes non ramifiées de degré premier d'un corps quadratique ⋮ The 3‐class groups of non‐Galois cubic fields—I ⋮ The 3‐class groups of non‐Galois cubic fields–II ⋮ Construction of hyperelliptic function fields of high three-rank ⋮ An algebraic approach to the growth of class numbers of binary quadratic lattices ⋮ Reading Gauss in the computer age: On the U.S. Reception of Gauss's number theoretical work (1938-1989) ⋮ Class Groups of Quadratic Fields ⋮ Zur Berechnung der Kapitulation in bikubischen Zahlkörpern

Cites Work

• Unnamed Item
• Über die Beziehung der Klassenzahlen quadratischer Körper zueinander.
• On Gauss's Class Number Problems
• Gauss's Ternary Form Reduction and the 2-Sylow Subgroup
• Extensions abéliennes non ramifiées de degré premier d'un corps quadratique
• A quadratic field of prime discriminant requiring three generators for its class group, and related theory
• Quadratic Fields with Four Invariants Divisible by 3
• On the Exponent of the Ideal Class Groups of Complex Quadratic Fields

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