CM-fields with cyclic ideal class groups of 2-power orders

DOI10.1006/jnth.1997.2179zbMath0881.11078OpenAlexW2049511570MaRDI QIDQ1376250

Stéphane R. Louboutin

Publication date: 18 December 1997

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1997.2179

zbMATH Keywords

zeta functionCM-fieldsrelative class numberscyclic ideal class groups of 2-power orders

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42) Other abelian and metabelian extensions (11R20)

Related Items

On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes ⋮ The CM class number one problem for curves of genus 2 ⋮ Corrigendum to: ``Real abelian fields satisfying the Hilbert-Speiser condition for some small primes \(p\). ⋮ The non-normal quartic CM-fields and the octic dihedral CM-fields with relative class number two ⋮ Determination of simple CM abelian surfaces defined over \(\mathbb{Q}\) ⋮ Class number problem for imaginary cyclic number fields ⋮ The imaginary abelian number fields of $2$-power degrees with ideal class groups of exponent $≤2$ ⋮ Determination of all \(\mathbb{Q}\)-rational CM-points in the moduli space of principally polarized abelian surfaces ⋮ Class numbers of imaginary abelian number fields

Cites Work

• Some analytic bounds for zeta functions and class numbers
• Some effective cases of the Brauer-Siegel theorem
• On the 2-component of the class group of certain cyclic extensions of degree \(2^ n\)
• Imaginary Abelian number fields with class number one
• Determination of all Imaginary Cyclic Quartic Fields with Class Number 2
• The Determination of all Imaginary, Quartic, Abelian Number Fields With Class Number 1
• L-Functions and Class Numbers of Imaginary Quadratic Fields and of Quadratic Extensions of an Imaginary Quadratic Field
• Lower Bounds for Relative Class Numbers of CM-Fields
• The Determination of the Imaginary Abelian Number Fields with Class Number One
• Determination of All Nonquadratic Imaginary Cyclic Number Fields of 2-Power Degrees with Ideal Class Groups of Exponents ≤2
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