The zeros of Dedekind zeta functions and class numbers of CM-fields

DOI10.1090/S0025-5718-08-02093-0zbMath1211.11126OpenAlexW2077935474MaRDI QIDQ3055078

Geon-No Lee, Soun-Hi Kwon

Publication date: 7 November 2010

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-08-02093-0

zbMATH Keywords

Dedekind zeta functionsArtin \(L\)-functionsCM-fieldsClass numbersrelative class numberszero-free regions of zeta and \(L\)-functions

Mathematics Subject Classification ID

Other number fields (11R21) 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) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Cites Work

• The class number one problem for some non-abelian normal CM-fields of degree 24
• CM-fields with relative class number one
• Minorations de discriminants [d’après A. M. Odlyzko]
• 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
• Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results
• Non-vanishing of \(L\)-functions and applications
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