Dirichlet series associated with strongly \(q\)-multiplicative functions
type: Item
instance of: scholarly article
title: Dirichlet series associated with strongly \(q\)-multiplicative functions
zbMATH Open document ID: 1060.11051
author: Giedrius Alkauskas
published in: The Ramanujan Journal
publication date: 2004-08-16T00:00:00Z
review text: Dirichlet series associated with the Thue-Morse sequence have been studied by \textit{J.-P. Allouche} and \textit{H. Cohen} [Bull. Lond. Math. Soc. 17, 531--538 (1985; Zbl 0577.10036)]. The case of series associated with general automatic sequences has been adressed by \textit{J.-P. Allouche}, \textit{M. Mendès France} and \textit{J. Peyrière} [J. Number Theory 81, No. 2, 359--373 (2000; Zbl 0971.11006)]. In the interesting paper under review, the author studies Dirichlet series associated with strongly \(q\)-multiplicative sequences whose average on \([0,q-1]\) is zero. Such series are known to have an analytic continuation to the whole plane [\textit{P. J. Grabner}, Acta. Arith. 65, No. 1, 85--96 (1993; Zbl 0783.11035)]. The author gives a different proof that also permits to prove that the order of these Dirichlet series is equal to 2. He also succeeds in proving that most of the trivial zeros of these series are simple.
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11A63
Mathematics Subject Classification ID: 11B85
zbMATH DE Number: 2091535
zbMATH Keywords: Dirichlet series
zbMATH Keywords: strongly \(q\)-multiplicative functions
zbMATH Keywords: order of functions
zbMATH Keywords: trivial zeros
reviewed by: Jean-Paul Allouche
MaRDI profile type: Publication
DOI: 10.1023/B:RAMA.0000027195.05101.2D
description: scientific article; zbMATH DE number 2091535