Upper bounds for residues of Dedekind zeta functions and class numbers of cubic and quartic number fields

DOI10.1090/S0025-5718-2011-02457-9zbMath1282.11150OpenAlexW2059972985MaRDI QIDQ3015059

Stéphane R. Louboutin

Publication date: 8 July 2011

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-2011-02457-9

zbMATH Keywords

class numberDedekind zeta functiondiscriminantnumber field

Mathematics Subject Classification ID

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

Related Items (6)

Explicit estimates for Artin \(L\)-functions: Duke's short-sum theorem and Dedekind zeta residues ⋮ Quadratic Chabauty for Atkin–Lehner quotients of modular curves of prime level and genus 4, 5, 6 ⋮ Heuristics and conjectures in the direction of a $p$-adic Brauer–Siegel Theorem ⋮ Small isospectral and nonisometric orbifolds of dimension 2 and 3 ⋮ Commensurability classes of fake quadrics ⋮ Upper bounds on residues of Dedekind zeta functions of non-normal totally real cubic fields

Cites Work

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• Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results
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• Explicit bounds for residues of Dedekind zeta functions, values of \(L\)-functions at \(s=1\), and relative class numbers

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