A survey of computational class field theory

DOI10.5802/jtnb.235zbMath0949.11063OpenAlexW2317648812MaRDI QIDQ1809036

Henri Cohen

Publication date: 14 August 2000

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

Full work available at URL: http://www.numdam.org/item?id=JTNB_1999__11_1_1_0

zbMATH Keywords

complex multiplicationclass field theoryHilbert's class fieldRay class field theory

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Complex multiplication and moduli of abelian varieties (11G15) Algebraic number theory computations (11Y40) Class field theory (11R37)

Related Items (3)

On the construction of class fields ⋮ Minimal ramifications ⋮ Constructing abelian extensions with prescribed norms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Euclidean fields having a large Lenstra constant
• Zur expliziten Berechnung von Ganzheitsbasen in Strahlklassenkörpern über einem imaginär-quadratischen Zahlkörper. (On the explicit calculation of integral bases in ray class fields over an imaginary quadratic number field)
• Subexponential algorithms for class group and unit computations
• Construction of ray class fields by elliptic units
• Class invariants by Shimura's reciprocity law
• Computing class fields via the Artin map
• Explicit Bounds for Primality Testing and Related Problems
• A polynomial reduction algorithm
• The structure of the multiplicative group of residue classes modulo
• Subgroup lattices and symmetric functions
• On the singular values of Weber modular functions
• Computing ray class groups, conductors and discriminants
• Hermite and Smith normal form algorithms over Dedekind domains
• Computing the Hilbert class field of real quadratic fields
• Problèmes de construction en multiplication complexe
• Algorithmic methods for finitely generated Abelian groups

This page was built for publication: A survey of computational class field theory