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

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.

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.

Reçu le :
Publié le :
DOI : https://doi.org/10.5802/jtnb.746
@article{JTNB_2010__22_3_771_0,
     author = {Alexey Zykin},
     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 = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.746/}
}
Alexey Zykin. Asymptotic properties of Dedekind zeta functions in families of number fields. Journal de Théorie des Nombres de Bordeaux, Tome 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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