The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for 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 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.
@article{JTNB_2010__22_3_771_0,
author = {Zykin, Alexey},
title = {Asymptotic properties of {Dedekind} zeta functions in families of number fields},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {771--778},
publisher = {Universit\'e Bordeaux 1},
volume = {22},
number = {3},
year = {2010},
doi = {10.5802/jtnb.746},
zbl = {1258.11095},
mrnumber = {2769345},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/jtnb.746/}
}
TY - JOUR AU - Zykin, Alexey TI - Asymptotic properties of Dedekind zeta functions in families of number fields JO - Journal de théorie des nombres de Bordeaux PY - 2010 SP - 771 EP - 778 VL - 22 IS - 3 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.746/ DO - 10.5802/jtnb.746 LA - en ID - JTNB_2010__22_3_771_0 ER -
%0 Journal Article %A Zykin, Alexey %T Asymptotic properties of Dedekind zeta functions in families of number fields %J Journal de théorie des nombres de Bordeaux %D 2010 %P 771-778 %V 22 %N 3 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.746/ %R 10.5802/jtnb.746 %G en %F JTNB_2010__22_3_771_0
Zykin, Alexey. 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. http://archive.numdam.org/articles/10.5802/jtnb.746/
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