Home > Proceedings > Adv. Stud. Pure Math. > Probability and Number Theory — Kanazawa 2005 > On the speed of convergence to limit distributions for Dedekind zeta-functions of non-Galois number fields
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VOL. 49 | 2007 On the speed of convergence to limit distributions for Dedekind zeta-functions of non-Galois number fields
Kohji Matsumoto

Editor(s) Shigeki Akiyama, Kohji Matsumoto, Leo Murata, Hiroshi Sugita

Abstract

We evaluate the speed of convergence in the Bohr-Jessen type of limit theorem on the value-distribution of Dedekind zeta-functions of number fields. When $K$ is a Galois number field, the Euler product of the corresponding Dedekind zeta-function $\zeta_K(s)$ is convex, hence the evaluation can be done similarly to the case of the Riemann zeta-function. However, when $K$ is non-Galois, some new ideas (based on the Artin-Chebotarev density theorem etc) are necessary, because the corresponding $\zeta_K(s)$ is not always convex.

Information

Published: 1 January 2007
First available in Project Euclid: 27 January 2019

zbMATH: 1228.11168
MathSciNet: MR2405605

Digital Object Identifier: 10.2969/aspm/04910199

Subjects:
Primary: 11R42
Secondary: 11K38