Non-abelian number fields with very large class numbers

DOI10.4064/aa125-3-2zbMath1158.11044OpenAlexW2097228594MaRDI QIDQ3414110

Ryan C. Daileda

Publication date: 5 January 2007

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa125-3-2

zbMATH Keywords

automorphic \(L\)-functionsArtin \(L\)-functionszero-density estimatesclass-numbernon-Abelian cubic fields

Mathematics Subject Classification ID

Cubic and quartic extensions (11R16) Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42) Automorphic forms, one variable (11F12)

Related Items (13)

Explicit estimates for Artin \(L\)-functions: Duke's short-sum theorem and Dedekind zeta residues ⋮ Moments of logarithmic derivatives of \(L\)-functions ⋮ Quartic fields with large class numbers ⋮ Unnamed Item ⋮ Dihedral and cyclic extensions with large class numbers ⋮ Extreme residues of Dedekind zeta functions ⋮ An approximate form of Artin's holomorphy conjecture and non-vanishing of Artin \(L\)-functions ⋮ Upper bounds for residues of Dedekind zeta functions and class numbers of cubic and quartic number fields ⋮ Minimal generators of the ideal class group ⋮ Maximal class numbers of CM number fields ⋮ Logarithmic derivatives of Artin -functions ⋮ Probabilistic properties of number fields ⋮ Genus theory and \(\varepsilon\)-conjectures on \(p\)-class groups

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