Some remarks on nonnegative multiplicative functions on arithmetic progressions
type: Item
instance of: scholarly article
title: Some remarks on nonnegative multiplicative functions on arithmetic progressions
zbMATH Open document ID: 0924.11077
author: Gennady Bachman
published in: Journal of Number Theory
publication date: 1999-03-22T00:00:00Z
review text: The distribution of general multiplicative functions on arithmetic progressions is a very difficult open problem. In this paper the author considers the simplest case of this problem and establishes an essentially best possible result of the form \[ \sum_{\substack{ n\leq x\\ n\equiv a\pmod q}} \frac{f(n)}{n}\ll \frac{1}{\varphi(q)} \sum_{\substack{ n\leq x\\ (n,q)=1}} \frac{f(n)}{n}, \] where \(f\) is a nonnegative multiplicative function and \((a,q)=1\).
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 1268046
zbMATH Keywords: multiplicative functions
zbMATH Keywords: arithmetic progressions
reviewed by: Jiahai Kan
MaRDI profile type: Publication
full work available at URL: jnth.1998.2279
OpenAlex ID: W2093187310
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cites work: Q4272975
DOI: 10.1006/JNTH.1998.2279
description: scientific article; zbMATH DE number 1268046