Computation of relative class numbers of CM-fields by using Hecke $L$-functions

DOI10.1090/S0025-5718-99-01096-0zbMath0931.11050OpenAlexW2052928783MaRDI QIDQ4700203

Stéphane R. Louboutin

Publication date: 1 November 1999

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01096-0

zbMATH Keywords

Hecke \(L\)-seriesHilbert class fieldclass number one problemquaternion extension

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Real zeros of (L(s, chi)); results on (L(1, chi)) (11M20) Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42) Software, source code, etc. for problems pertaining to number theory (11-04)

Related Items (8)

The class number one problem for some non-abelian normal CM-fields of degree 48 ⋮ The class number one problem for the normal CM-fields of degree 32 ⋮ NONABELIAN NORMAL CM-FIELDS OF DEGREE 2 pq ⋮ Class number one problem for normal CM-fields ⋮ Dihedral CM fields with class number one ⋮ On the history of the study of ideal class groups ⋮ Efficient computation of root numbers and class numbers of parametrized families of real abelian number fields ⋮ Computation of class numbers of quadratic number fields

Cites Work

• A Kronecker limit formula for real quadratic fields
• An elementary proof for a theorem of Thomas and Vasquez
• Computation of class numbers of number fields
• On evaluation of \(L\)-functions over real quadratic fields
• Sur l'arithmétique des extensions galoisiennes à groupe de Galois diédral d'ordre \(2p\)
• On the functional equation of the Artin L-function for characters of real representations
• Artin-root numbers and normal integral bases for quaternion fields
• Minoration au point 1 des fonctions L et détermination des corps sextiques abéliens totalement imaginaires principaux
• Computation of Relative Class Numbers of Imaginary Abelian Number Fields
• Construction of the real dihedral number fields of degree 2p. Applications
• Computation of relative class numbers of CM-fields
• The class number one problem for some non-abelian normal CM-fields
• Determination of all Quaternion Octic CM-Fields with Class Number 2
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