The class number one problem for some non-abelian normal CM-fields

DOI10.1090/S0002-9947-97-01768-6zbMath0893.11045OpenAlexW1663136107MaRDI QIDQ4372562

Ryotaro Okazaki, Michel Olivier, Stéphane R. Louboutin

Publication date: 16 December 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-97-01768-6

zbMATH Keywords

class numberrelative class numberDedekind zeta-functiondihedral fieldlower bounds for discriminantsnon-abelian normal CM-fields of degree 12

Mathematics Subject Classification ID

Other number fields (11R21) 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 (18)

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 ⋮ Unnamed Item ⋮ Thue equations and CM-fields ⋮ The CM-fields with class number one which are Hilbert class fields of quadratic fields ⋮ Class number one problem for normal CM-fields ⋮ The class number one problem for imaginary octic non-CM extensions of \(\mathbb{Q}\) ⋮ Computation of relative class numbers of CM-fields ⋮ Dihedral CM fields with class number one ⋮ Computation of L(0, χ) and of relative class numbers of CM-fields ⋮ The class number one problem for some non-abelian normal CM-fields of degree 24 ⋮ Tame Galois module structure revisited ⋮ Computation of relative class numbers of CM-fields by using Hecke $L$-functions ⋮ Note on Bernoulli numbers associated to some Dirichlet character of prime conductor ⋮ CM-fields with relative class number one ⋮ Class number problem for imaginary cyclic number fields ⋮ Class numbers of imaginary abelian number fields

Cites Work

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• Norme relative de l'unité fondamentale et 2-rang du groupe des classes d'idéaux de certains corps biquadratiques
• The Determination of all Imaginary, Quartic, Abelian Number Fields With Class Number 1
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• Lower Bounds for Relative Class Numbers of CM-Fields
• The Determination of the Imaginary Abelian Number Fields with Class Number One
• Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one
• Notes on small class numbers
• The imaginary bicyclic biquadratic fields with class-number 1.
• Class Numbers of Totally Imaginary Quadratic Extensions of Totally Real Fields
• Some analytic estimates of class numbers and discriminants

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