On the distribution of complex-valued multiplicative functions
type: Item
instance of: scholarly article
title: On the distribution of complex-valued multiplicative functions
zbMATH Open document ID: 0864.11039
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1996-08-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/230142
full work available at URL: jtnb8-1.html
review text: Let \(g_1,g_2\) be complex-valued multiplicative functions. The author finds a sufficient and necessary condition for \(g_1,g_2\) to have a joint limiting distribution. This is expressed in terms of sums involving \(u_g(p)= g(p)/ |g(p) |\) if \(g(p) \neq 0\), 0 if \(g(p)=0\) and \(v_g(p)=\log |g(p) |\) if \(|g(p) |\in(e^{-1},e)\) 1 otherwise. This result is less general than that of \textit{J.-L. Mauclaire} [Acta Arith. 68, 201-212 (1994; Zbl 0830.11029)], where the corresponding problem is solved in every locally compact commutative group, though the translation between them is not completely obvious because they are expressed in different terms.
Mathematics Subject Classification ID: 11K65
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 912506
zbMATH Keywords: multiplicative functions
zbMATH Keywords: joint limiting distribution
author: Antanas Laurinčikas
reviewed by: Imre Z. Ruzsa
MaRDI profile type: Publication
OpenAlex ID: W2007119577
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DOI: 10.5802/JTNB.164
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description: scientific article; zbMATH DE number 912506