# Asymptotic properties of Dedekind zeta functions in families of number fields

Alexey Zykin^{[1]}

- [1] State University — Higher School of Economics, 7, Vavilova st. 117312, Moscow, Russia

Journal de Théorie des Nombres de Bordeaux (2010)

- Volume: 22, Issue: 3, page 771-778
- ISSN: 1246-7405

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topZykin, Alexey. "Asymptotic properties of Dedekind zeta functions in families of number fields." Journal de Théorie des Nombres de Bordeaux 22.3 (2010): 771-778. <http://eudml.org/doc/116434>.

@article{Zykin2010,

abstract = {The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for $\Re s > 1/2$ 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.},

affiliation = {State University — Higher School of Economics, 7, Vavilova st. 117312, Moscow, Russia},

author = {Zykin, Alexey},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {Dedekind zeta function; asymptotically exact families},

language = {eng},

number = {3},

pages = {771-778},

publisher = {Université Bordeaux 1},

title = {Asymptotic properties of Dedekind zeta functions in families of number fields},

url = {http://eudml.org/doc/116434},

volume = {22},

year = {2010},

}

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

PB - Université Bordeaux 1

VL - 22

IS - 3

SP - 771

EP - 778

AB - The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for $\Re s > 1/2$ 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.

LA - eng

KW - Dedekind zeta function; asymptotically exact families

UR - http://eudml.org/doc/116434

ER -

## References

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- A. Zykin, Asymptotic properties of zeta functions over finite fields. Preprint. Zbl1329.14056

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