The class number one problem for some non-normal CM-fields of degree \(2p\)

DOI10.1016/j.jnt.2012.02.020zbMath1275.11143OpenAlexW2004030495MaRDI QIDQ423629

Jeoung-Hwan Ahn, Soun-Hi Kwon, Gérard Boutteaux, Stéphane R. Louboutin

Publication date: 4 June 2012

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2012.02.020

zbMATH Keywords

class numberDedekind zeta functionCM-field

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42)

Related Items (2)

On the Splitting Field of Some Polynomials with Class Number One ⋮ Real zeros of Dedekind zeta functions

Uses Software

• GAP

Cites Work

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• Approximate formulae for L(1,χ)
• Powerful Necessary Conditions for Class Number Problems
• CM-fields with relative class number one
• Explicit Bounds for Primality Testing and Related Problems
• 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
• Computation of relative class numbers of CM-fields
• The Class Number One Problem for Some Non-Abelian Normal CM-Fields of 2-Power Degrees
• Bounds for the degrees of CM-fields of class number one
• Explicit Lower bounds for residues at 𝑠=1 of Dedekind zeta functions and relative class numbers of CM-fields
• Determination of all Quaternion Octic CM-Fields with Class Number 2

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