On the characterization of complex-valued multiplicative functions. II
type: Item
instance of: scholarly article
title: On the characterization of complex-valued multiplicative functions. II
zbMATH Open document ID: 0569.10027
DOI: 10.1007/BF01955034
author: Katalin Kovács
published in: Acta Mathematica Hungarica
publication date: 1985-01-01T00:00:00Z
review text: [Part I, cf. ibid. 44, 401-406 (1984; Zbl 0562.10024).] The article contains the proof of the following theorem: Let \(f: {\mathbb{N}}\to {\mathbb{C}}\) be multiplicative. To any \(h: {\mathbb{N}}\to {\mathbb{R}}\) there exists a sequence \(A=\{a_ 1<a_ 2<...\}\), such that \(a_ n>h(n)\) and if at least two of the functions \(| f|\), Re f and Im f are monotonic on A, then \(f(n)=n^ k\) (except for some special cases).
Mathematics Subject Classification ID: 11K65
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 3908532
zbMATH Keywords: characterization of complex-valued multiplicative functions
zbMATH Keywords: rare sets
MaRDI profile type: Publication
cites work: On the distribution function of additive functions
cites work: On additive functions which are monotone on a „Rare” set
cites work: On the characterization of complex-valued multiplicative functions. I
cites work: On Monotone Multiplicative Functions
full work available at URL: https://doi.org/10.1007/bf01955034
OpenAlex ID: W1991929502
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description: scientific article; zbMATH DE number 3908532