Computing the Hilbert class field of real quadratic fields

DOI10.1090/S0025-5718-99-01111-4zbMath1042.11075MaRDI QIDQ4955872

Henri Cohen, Xavier-François Roblot

Publication date: 22 May 2000

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

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Class field theory (11R37) Zeta functions and (L)-functions of number fields (11R42) Analytic computations (11Y35)

Related Items (6)

Stark's conjecture over complex cubic number fields ⋮ Continued fractions, special values of the double sine function, and Stark units over real quadratic fields ⋮ Arithmetic twists and Abelian extensions ⋮ Stark's Conjectures and Hilbert's Twelfth Problem ⋮ Topics in computational algebraic number theory ⋮ A survey of computational class field theory

Uses Software

• PARI/GP

Cites Work

• The Stark conjectures on Artin \(L\)-functions at \(s=0\). Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher.
• A note on the splitting of the Hilbert class field
• Generalized exponential operators in the continuation of the confluent hypergeometric functions
• \(L\)-functions at \(s=1\). IV: First derivatives at \(s=0\)
• The genus fields of algebraic number fields
• A general method for an accurate evaluation of exponential integrals \(E_1(x)\), \(x>0\)
• The determination of incomplete gamma functions through analytic integration
• On computing subfields
• Computing class fields via the Artin map
• A polynomial reduction algorithm
• Computing ray class groups, conductors and discriminants
• Explicit bounds for primes in residue classes
• Problèmes de construction en multiplication complexe
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