Computing class fields via the Artin map

DOI10.1090/S0025-5718-00-01255-2zbMath0982.11074MaRDI QIDQ2719081

Claus Fieker

Publication date: 14 May 2001

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

zbMATH Keywords

Kummer extensionArtin mapcomputation of class fields

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Class field theory (11R37)

Related Items

Minimal discriminants for fields with small Frobenius groups as Galois groups., Computing the multiplicative group of residue class rings, Constructing class fields over local fields, A Database for Field Extensions of the Rationals, The distribution of second \(p\)-class groups on coclass graphs, On the construction of class fields, Cyclic extensions of prime degree and their \(p\)-adic regulators, 3-class field towers of exact length 3, Minimal ramifications, Topics in computational algebraic number theory, Minimizing representations over number fields. II: Computations in the Brauer group., Computing the Hilbert class field of real quadratic fields, Valuations of \(p\)-adic regulators of cyclic cubic fields, A survey of computational class field theory, The group Gal(k3(2)|k) for k = ℚ(−3,d) of type (3,3), Algebraic number fields generated by an infinite family of monogenic trinomials, Principalization algorithm via class group structure, Constructing abelian extensions with prescribed norms

Cites Work

• 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)
• On the computation of Hilbert class fields
• Computing automorphisms of abelian number fields
• Computing Stark units for totally real cubic fields
• Computing ray class groups, conductors and discriminants
• Explicit bounds for primes in residue classes
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