Remarks on an elementary proof of Halász's theorem
type: Item
instance of: scholarly article
title: Remarks on an elementary proof of Halász's theorem
zbMATH Open document ID: 0829.11046
DOI: 10.1007/BF00995986
published in: Lithuanian Mathematical Journal
publication date: 1995-09-18T00:00:00Z
review text: A fundamental theorem of \textit{G. Halász} [Acta Math. Acad. Sci. Hung. 19, 365-403 (1968; Zbl 0165.058)] describes those multiplicative functions that satisfy \(|f(n) |\leq 1\) and have a mean value. \textit{H. Daboussi} and the author [Math. Z. 209, 43-52 (1992; Zbl 0736.11053)] gave a new proof of this result. Here a part of this proof is simplified. It should be noted that this proof is not completely `elementary' in the usual sense: complex functions are applied, though definitely less heavily than in the classical `analytical' proof.
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11K65
zbMATH DE Number: 794499
zbMATH Keywords: Halász's theorem
zbMATH Keywords: multiplicative functions
zbMATH Keywords: mean value
author: K.-H. Indlekofer
reviewed by: Imre Z. Ruzsa
MaRDI profile type: Publication
cites work: Two elementary proofs of Halász's theorem
cites work: Sur les fonctions arithmétiques multiplicatives
cites work: Q3867876
cites work: Some unsolved problems
cites work: Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen
cites work: Q3839703
cites work: On Wirsing's mean value Theorem for Multiplicative Functions
cites work: A mean-value theorem for multiplicative functions
cites work: Das asymptotische Verhalten von Summen über multiplikative Funktionen. II
full work available at URL: https://doi.org/10.1007/bf00995986
OpenAlex ID: W1966277449
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description: scientific article; zbMATH DE number 794499