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

Louboutin, Stéphane

doi:10.1090/S0025-5718-2011-02457-9

Upper bounds for residues of Dedekind zeta functions and class numbers of cubic and quartic number fields
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by Stéphane R. Louboutin PDF

Math. Comp. 80 (2011), 1813-1822 Request permission

Abstract:

Let $K$ be an algebraic number field. Assume that $\zeta _K(s)/\zeta (s)$ is entire. We give an explicit upper bound for the residue at $s=1$ of the Dedekind zeta function $\zeta _K(s)$ of $K$. We deduce explicit upper bounds on class numbers of cubic and quartic number fields.

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