A remark on Dedekind zeta functions and the \(K\)-group
type: Item
instance of: scholarly article
title: A remark on Dedekind zeta functions and the \(K\)-group
zbMATH Open document ID: 0712.11069
DOI: 10.1007/BF01198112
author: Keiichi Komatsu
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: Assume \(k\) and \(k'\) are two number fields having the same Dedekind zeta function. Let \(L\) be a (common) Galois-closure and \(p\) a prime not dividing \([L:k]\). The author shows that for all \(n\geq 0\) the \(p\)-primary components of the \(K\)-groups of the rings of integers of \(k\) and \(k'\) are isomorphic. The result is easily obtained from the case \(n=0\), which is due to \textit{R. Perlis} [J. Number Theory 10, 489--509 (1978; Zbl 0393.12009)].
reviewed by: Manfred Kolster
Mathematics Subject Classification ID: 11R70
Mathematics Subject Classification ID: 11R42
Mathematics Subject Classification ID: 19F27
zbMATH DE Number: 4171055
zbMATH Keywords: Dedekind zeta function
zbMATH Keywords: K-groups
zbMATH Keywords: rings of integers
MaRDI profile type: Publication
cites work: On the class numbers of arithmetically equivalent fields
cites work: Higher algebraic K-theory: I
full work available at URL: https://doi.org/10.1007/bf01198112
OpenAlex ID: W2032642771
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description: scientific article; zbMATH DE number 4171055