Asymptotic properties of Dedekind zeta functions in families of number fields
Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 3, pp. 771-778.

The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for s>1/2 in families of number fields, assuming that the Generalized Riemann Hypothesis holds. This result can be viewed as a generalization of the Brauer–Siegel theorem. As an application we obtain a limit formula for Euler–Kronecker constants in families of number fields.

Le but de cet article est de démontrer une formule qui exprime le comportement asymptotique de la fonction zêta de Dedekind dans des familles de corps globaux pour s>1/2 en supposant que l’Hypothèse de Riemann Généralisée est vérifiée. On peut voir ce résultat comme une généralisation du théorème de Brauer-Siegel. Comme corollaire, on obtient une formule limite pour les constants d’Euler-Kronecker dans des familles de corps globaux.

Received:
Published online:
DOI: 10.5802/jtnb.746
Alexey Zykin 1

1 State University — Higher School of Economics, 7, Vavilova st. 117312, Moscow, Russia
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Alexey Zykin. Asymptotic properties of Dedekind zeta functions in families of number fields. Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 3, pp. 771-778. doi : 10.5802/jtnb.746. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.746/

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