Distribution of the values of a sum of additive functions with shifted arguments
type: Item
instance of: scholarly article
title: Distribution of the values of a sum of additive functions with shifted arguments
zbMATH Open document ID: 0802.11030
DOI: 10.1007/BF01236629
author: Kh. Kh. Usmanov
author: Nikolai M. Timofeev
published in: Mathematical Notes
publication date: 1994-07-21T00:00:00Z
review text: A necessary and sufficient condition is found for a couple of additive functions \(g_ 1\), \(g_ 2\) to have the property that \(g_ 1(n)+ g_ 2(n+1)\) has a limiting distribution with a suitable centering. This extends a result of \textit{A. Hildebrand} [Trans. Am. Math. Soc. 310, 257- 276 (1988; Zbl 0707.11057)], where \(g(n+1)- g(n)\) is considered. The condition is equivalent to saying that the functions themselves have limiting distributions under suitable centering.
Mathematics Subject Classification ID: 11K65
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11N64
zbMATH DE Number: 578699
zbMATH Keywords: additive functions
zbMATH Keywords: limiting distribution
zbMATH Keywords: centering
reviewed by: Imre Z. Ruzsa
MaRDI profile type: Publication
cites work: An Erdos-Wintner Theorem for Differences of Additive Functions
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full work available at URL: https://doi.org/10.1007/bf01236629
OpenAlex ID: W1986406166
description: scientific article; zbMATH DE number 578699