Zeta functions of integral representations of cyclic \(p\)-groups.
type: Item
instance of: scholarly article
title: Zeta functions of integral representations of cyclic \(p\)-groups.
zbMATH Open document ID: 1052.20006
DOI: 10.1016/S0021-8693(03)00422-8
author: Christian Wittmann
published in: Journal of Algebra
publication date: 2004-05-27T00:00:00Z
review text: Let \(p\) be a prime number and \(C_{p^k}\) be a cyclic group of order \(p^k\). Let \(L\) be a finitely generated torsion free \(\mathbb{Z}[C_{p^k}]\)-module. \textit{L. Solomon} [Adv. Math. 26, 306-326 (1977; Zbl 0374.20007)] introduced a zeta function attached to \(L\). Calculation of this zeta function can be reduced to calculation of the zeta function of the free \(\mathbb{Z}_p[C_{p^k}]\)-module \(\mathbb{Z}_p[C_{p^k}]^n\). It is developed a recursion formula, which yields some new explicit formulas for the zeta function of \(\mathbb{Z}_p[C_{p^k}]^n\) in the cases \(k=1\), \(2\) and \(n\geq 1\), and \(k=3\), \(n=1\). An important combinatorial tool for these computations is the Möbius function of a partially ordered set.
Mathematics Subject Classification ID: 20C10
Mathematics Subject Classification ID: 20C11
Mathematics Subject Classification ID: 16H05
Mathematics Subject Classification ID: 11R42
Mathematics Subject Classification ID: 11S40
Mathematics Subject Classification ID: 06B05
zbMATH DE Number: 2066834
zbMATH Keywords: zeta functions
zbMATH Keywords: modules over group rings
zbMATH Keywords: integral representations
zbMATH Keywords: Möbius functions
reviewed by: Kanat Abdukhalikov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2066834